Artículos de revistas: "Discret soliton"

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Xu, Haitao, Zhelang Pan, Zhihuan Luo, Yan Liu, Suiyan Tan, Zhijie Mai y Jun Xu. "Zigzag Solitons and Spontaneous Symmetry Breaking in Discrete Rabi Lattices with Long-Range Hopping". Symmetry 10, n.º 7 (12 de julio de 2018): 277. http://dx.doi.org/10.3390/sym10070277.

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A new type of discrete soliton, which we call zigzag solitons, is founded in two-component discrete Rabi lattices with long-range hopping. The spontaneous symmetry breaking (SSB) of zigzag solitons is also studied. Through numerical simulation, we found that by enhancing the intensity of the long-range linearly-coupled effect or increasing the total input power, the SSB process from the symmetric soliton to the asymmetric soliton will switch from the supercritical to subcritical type. These results can help us better understand both the discrete solitons and the Rabi coupled effect.

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Wang, Yutian, Fanglin Chen, Songnian Fu, Jian Kong, Andrey Komarov, Mariusz Klimczak, Ryszard BuczyČski, Xiahui Tang, Ming Tang y Luming Zhao. "Nonlinear Fourier transform assisted high-order soliton characterization". New Journal of Physics 24, n.º 3 (1 de marzo de 2022): 033039. http://dx.doi.org/10.1088/1367-2630/ac5a86.

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Abstract Nonlinear Fourier transform (NFT), based on the nonlinear Schrödinger equation, is implemented for the description of soliton propagation, and in particular focused on propagation of high-order solitons. In nonlinear frequency domain, a high-order soliton has multiple eigenvalues depending on the soliton amplitude and pulse-width. During the propagation along the standard single mode fiber (SSMF), their eigenvalues remain constant, while the corresponding discrete spectrum rotates along with the SSMF transmission. Consequently, we can distinguish the soliton order based on its eigenvalues. Meanwhile, the discrete spectrum rotation period is consistent with the temporal evolution period of the high-order solitons. The discrete spectrum contains nearly 99.99% energy of a soliton pulse. After inverse-NFT on discrete spectrum, soliton pulse can be reconstructed, illustrating that the eigenvalues can be used to characterize soliton pulse with good accuracy. This work shows that soliton characteristics can be well described in the nonlinear frequency domain. Moreover, as a significant supplement to the existing means of characterizing soliton pulses, NFT is expected to be another fundamental optical processing method besides an oscilloscope (measuring pulse time domain information) and a spectrometer (measuring pulse frequency domain information).

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Teutsch, Ina, Markus Brühl, Ralf Weisse y Sander Wahls. "Contribution of solitons to enhanced rogue wave occurrence in shallow depths: a case study in the southern North Sea". Natural Hazards and Earth System Sciences 23, n.º 6 (7 de junio de 2023): 2053–73. http://dx.doi.org/10.5194/nhess-23-2053-2023.

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Abstract. The shallow waters off the coast of Norderney in the southern North Sea are characterised by a higher frequency of rogue wave occurrences than expected. Here, rogue waves refer to waves exceeding twice the significant wave height. The role of nonlinear processes in the generation of rogue waves at this location is currently unclear. Within the framework of the Korteweg–de Vries (KdV) equation, we investigated the discrete soliton spectra of measured time series at Norderney to determine differences between time series with and without rogue waves. For this purpose, we applied a nonlinear Fourier transform (NLFT) based on the Korteweg–de Vries equation with vanishing boundary conditions (vKdV-NLFT). At measurement sites where the propagation of waves can be described by the KdV equation, the solitons in the discrete nonlinear vKdV-NLFT spectrum correspond to physical solitons. We do not know whether this is the case at the considered measurement site. In this paper, we use the nonlinear spectrum to classify rogue wave and non-rogue wave time series. More specifically, we investigate if the discrete nonlinear spectra of measured time series with visible rogue waves differ from those without rogue waves. Whether or not the discrete part of the nonlinear spectrum corresponds to solitons with respect to the conditions at the measurement site is not relevant in this case, as we are not concerned with how these spectra change during propagation. For each time series containing a rogue wave, we were able to identify at least one soliton in the nonlinear spectrum that contributed to the occurrence of the rogue wave in that time series. The amplitudes of these solitons were found to be smaller than the crest height of the corresponding rogue wave, and interaction with the continuous wave spectrum is needed to fully explain the observed rogue wave. Time series with and without rogue waves showed different characteristic soliton spectra. In most of the spectra calculated from rogue wave time series, most of the solitons clustered around similar heights, but the largest soliton was outstanding, with an amplitude significantly larger than all other solitons. The presence of a clearly outstanding soliton in the spectrum was found to be an indicator pointing towards the enhanced probability of the occurrence of a rogue wave in the time series. Similarly, when the discrete spectrum appears as a cluster of solitons without the presence of a clearly outstanding soliton, the presence of a rogue wave in the observed time series is unlikely. These results suggest that soliton-like and nonlinear processes substantially contribute to the enhanced occurrence of rogue waves off Norderney.

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SINGER, ANDREW C. y ALAN V. OPPENHEIM. "CIRCUIT IMPLEMENTATIONS OF SOLITON SYSTEMS". International Journal of Bifurcation and Chaos 09, n.º 04 (abril de 1999): 571–90. http://dx.doi.org/10.1142/s0218127499000419.

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Recently, a large class of nonlinear systems which possess soliton solutions has been discovered for which exact analytic solutions can be found. Solitons are eigenfunctions of these systems which satisfy a form of superposition and display rich signal dynamics as they interact. In this paper, we view solitons as signals and consider exploiting these systems as specialized signal processors which are naturally suited to a number of complex signal processing tasks. New circuit models are presented for two soliton systems, the Toda lattice and the discrete-KdV equations. These analog circuits can generate and process soliton signals and can be used as multiplexers and demultiplexers in a number of potential soliton-based wireless communication applications discussed in [Singer et al.]. A hardware implementation of the Toda lattice circuit is presented, along with a detailed analysis of the dynamics of the system in the presence of additive Gaussian noise. This circuit model appears to be the first such circuit sufficiently accurate to demonstrate true overtaking soliton collisions with a small number of nodes. The discrete-KdV equation, which was largely ignored for having no prior electrical or mechanical analog, provides a convenient means for processing discrete-time soliton signals.

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Jia, Yuechen, Yu Lu, Miao Yu y Hasi Gegen. "M -Breather, Lumps, and Soliton Molecules for the 2 + 1 -Dimensional Elliptic Toda Equation". Advances in Mathematical Physics 2021 (24 de junio de 2021): 1–18. http://dx.doi.org/10.1155/2021/5211451.

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The 2 + 1 -dimensional elliptic Toda equation is a higher dimensional generalization of the Toda lattice and also a discrete version of the Kadomtsev-Petviashvili-1 (KP1) equation. In this paper, we derive the M -breather solution in the determinant form for the 2 + 1 -dimensional elliptic Toda equation via Bäcklund transformation and nonlinear superposition formulae. The lump solutions of the 2 + 1 -dimensional elliptic Toda equation are derived from the breather solutions through the degeneration process. Hybrid solutions composed of two line solitons and one breather/lump are constructed. By introducing the velocity resonance to the N -soliton solution, it is found that the 2 + 1 -dimensional elliptic Toda equation possesses line soliton molecules, breather-soliton molecules, and breather molecules. Based on the N -soliton solution, we also demonstrate the interactions between a soliton/breather-soliton molecule and a lump and the interaction between a soliton molecule and a breather. It is interesting to find that the KP1 equation does not possess a line soliton molecule, but its discrete version—the 2 + 1 -dimensional elliptic Toda equation—exhibits line soliton molecules.

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Wu, Xiao-Yu, Bo Tian, Lei Liu y Yan Sun. "Discrete Solitons and Bäcklund Transformation for the Coupled Ablowitz–Ladik Equations". Zeitschrift für Naturforschung A 72, n.º 10 (26 de septiembre de 2017): 963–72. http://dx.doi.org/10.1515/zna-2017-0196.

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AbstractUnder investigation in this paper are the coupled Ablowitz–Ladik equations, which are linked to the optical fibres, waveguide arrays, and optical lattices. Binary Bell polynomials are applied to construct the bilinear forms and bilinear Bäcklund transformation. Bright/dark one- and two-soliton solutions are also obtained. Asymptotic analysis indicates that the interactions between the bright/dark two solitons are elastic. Amplitudes and velocities of the bright solitons increase as the value of the lattice spacing increases. Increasing value of the lattice spacing can lead to the increase of both the bright solitons’ amplitudes and velocities, and the decrease of the velocities of the dark solitons. The lattice spacing parameter has no effect on the amplitudes of the dark solitons. Overtaking interaction between the unidirectional bright two solitons and a bound state of the two equal-velocity solitons is presented. Overtaking interaction between the unidirectional dark two solitons and the two parallel dark solitons is also plotted.

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Sekulic, Dalibor L., Natasa M. Samardzic, Zivorad Mihajlovic y Miljko V. Sataric. "Soliton Waves in Lossy Nonlinear Transmission Lines at Microwave Frequencies: Analytical, Numerical and Experimental Studies". Electronics 10, n.º 18 (17 de septiembre de 2021): 2278. http://dx.doi.org/10.3390/electronics10182278.

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In this paper, we performed analytical, numerical and experimental studies on the generation of soliton waves in discrete nonlinear transmission lines (NLTL) with varactors, as well as the analysis of the losses impact on the propagation of these waves. Using the reductive perturbation method, we derived a nonlinear Schrödinger (NLS) equation with a loss term and determined an analytical expression that completely describes the bright soliton profile. Our theoretical analysis predicts the carrier wave frequency threshold above which a formation of bright solitons can be observed. We also performed numerical simulations to confirm our analytical results and we analyzed the space–time evolution of the soliton waves. A good agreement between analytical and numerical findings was obtained. An experimental prototype of the lossy NLTL, built at the discrete level, was used to validate our proposed model. The experimental shape of the envelope solitons is well fitted by the theoretical waveforms, which take into account the amplitude damping due to the losses in commercially available varactors and inductors used in a prototype. Experimentally observed changes in soliton amplitude and half–maximum width during the propagation along lossy NLTL are in good accordance with the proposed model defined by NLS equation with loss term.

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Konyukhov, Andrey I. "Transformation of Eigenvalues of the Zakharov–Shabat Problem under the Effect of Soliton Collision". Izvestiya of Saratov University. New series. Series: Physics 20, n.º 4 (2020): 248–57. http://dx.doi.org/10.18500/1817-3020-2020-20-4-248-257.

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Background and Objectives: The Zakharov–Shabat spectral problem allows to find soliton solutions of the nonlinear Schrodinger equation. Solving the Zakharov–Shabat problem gives both a discrete set of eigenvalues λj and a continuous one. Each discrete eigenvalue corresponds to an individual soliton with the real part Re(λj) providing the soliton velocity and the imaginary part Im(λj) determining the soliton amplitude. Solitons can be used in optical communication lines to compensate both non-linearity and dispersion. However, a direct use of solitons in return-to-zero signal encoding is inhibited. The interaction between solitions leads to the loss of transmitted data. The problem of soliton interaction can be solved using eigenvalues. The latter do not change when the solitons obey the nonlinear Schrodinger equation. Eigenvalue communication was realized recently using electronic signal processing. To increase the transmission speed the all-optical method for controlling eigenvalues should be developed. The presented research is useful to develop optical methods for the transformation of the eigenvalues. The purpose of the current paper is twofold. First, we intend to clarify the issue of whether the dispersion perturbation can not only split a bound soliton state but join solitons into a short oscillating period breather. The second goal of the paper is to describe the complicated dynamics and mutual interaction of complex eigenvalues of the Zakharov–Shabat spectral problem. Materials and Methods: Pulse propagation in single-mode optical fibers with a variable core diameter can be described using the nonlinear Schrödinger equation (NLSE) which coefficients depends on the evolution coordinate. The NLSE with the variable dispersion coefficient was considered. The dispersion coefficient was described using a hyperbolic tangent function. The NLSE and the Zakharov– Shabat spectral problem were solved using the split-step method and the layer-peeling method, respectively. Results: The results of numerical analysis of the modification of soliton pulses under the effect of variable dispersion coefficient are presented. The main attention is paid to the process of transformation of eigenvalues of the Zakharov–Shabat problem. Collision of two in-phase solitons, which are characterized by two complex eigenvalues is considered. When the coefficients of the nonlinear Schrodinger equation change, the collision of the solitons becomes inelastic. The inelastic collision is characterized by the change of the eigenvalues. It is shown that the variation of the coefficients of the NLSE allows to control both real and imaginary parts of the eigenvalues. Two scenarios for the change of the eigenvalues were identified. The first scenario is characterized by preserving the zero real part of the eigenvalues. The second one is characterized by the equality of their imaginary parts. The transformation of eigenvalues is most effective at the distance where the field spectrum possesses a two-lobe shape. Variation of the NLSE coefficient can introduce splitting or joining of colliding soliton pulses. Conclusion: The presented results show that the eigenvalues can be changed only with a small variation of the NLSE coefficients. On the one hand, a change in the eigenvalues under the effect of inelastic soliton collision is an undesirable effect since the inelastic collision of solitons will lead to unaccounted modulation in soliton optical communication links. On the other hand, the dependence of the eigenvalues on the parameters of the colliding solitons allows to modulate the eigenvalues using all-fiber optical devices. Currently, the modulation of the eigenvalues is organized using electronic devices. Therefore, the transmission of information is limited to nanosecond pulses. For picosecond pulse communication, the development of all-optical modulation methods is required. The presented results will be useful in the development of methods for controlling optical solitons and soliton states of the Bose–Einstein condensate.

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Zhong, Rong-Xuan, Nan Huang, Huang-Wu Li, He-Xiang He, Jian-Tao Lü, Chun-Qing Huang y Zhao-Pin Chen. "Matter-wave solitons supported by quadrupole–quadrupole interactions and anisotropic discrete lattices". International Journal of Modern Physics B 32, n.º 09 (5 de abril de 2018): 1850107. http://dx.doi.org/10.1142/s0217979218501072.

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We numerically and analytically investigate the formations and features of two-dimensional discrete Bose–Einstein condensate solitons, which are constructed by quadrupole–quadrupole interactional particles trapped in the tunable anisotropic discrete optical lattices. The square optical lattices in the model can be formed by two pairs of interfering plane waves with different intensities. Two hopping rates of the particles in the orthogonal directions are different, which gives rise to a linear anisotropic system. We find that if all of the pairs of dipole and anti-dipole are perpendicular to the lattice panel and the line connecting the dipole and anti-dipole which compose the quadrupole is parallel to horizontal direction, both the linear anisotropy and the nonlocal nonlinear one can strongly influence the formations of the solitons. There exist three patterns of stable solitons, namely horizontal elongation quasi-one-dimensional discrete solitons, disk-shape isotropic pattern solitons and vertical elongation quasi-continuous solitons. We systematically demonstrate the relationships of chemical potential, size and shape of the soliton with its total norm and vertical hopping rate and analytically reveal the linear dispersion relation for quasi-one-dimensional discrete solitons.

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Liu, Nan y Xiao-Yong Wen. "Dynamics and elastic interactions of the discrete multi-dark soliton solutions for the Kaup–Newell lattice equation". Modern Physics Letters B 32, n.º 07 (5 de marzo de 2018): 1850085. http://dx.doi.org/10.1142/s0217984918500859.

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Under consideration in this paper is the Kaup–Newell (KN) lattice equation which is an integrable discretization of the KN equation. Infinitely, many conservation laws and discrete N-fold Darboux transformation (DT) for this system are constructed and established based on its Lax representation. Via the resulting N-fold DT, the discrete multi-dark soliton solutions in terms of determinants are derived from non-vanishing background. Propagation and elastic interaction structures of such solitons are shown graphically. Overtaking interaction phenomena between/among the two, three and four solitons are discussed. Numerical simulations are used to explore their dynamical behaviors of such multi-dark solitons. Numerical results show that their evolutions are stable against a small noise. Results in this paper might be helpful for understanding the propagation of nonlinear Alfvén waves in plasmas.

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Wang, Hao-Tian y Xiao-Yong Wen. "Dynamics of multi-soliton and breather solutions for a new semi-discrete coupled system related to coupled NLS and coupled complex mKdV equations". Modern Physics Letters B 32, n.º 28 (4 de octubre de 2018): 1850340. http://dx.doi.org/10.1142/s0217984918503402.

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In this paper, a new semi-discrete coupled system which was firstly proposed by Bronsard and Pelinovsky is under investigation. Based on its known Lax pair, the infinitely-many conservation laws and discrete N-fold DT for this system are constructed. As applications, bell-shaped multi-soliton and breather solutions in terms of determinants for this system are firstly derived by means of the discrete N-fold DT. Propagation and elastic interaction structures of such soliton solutions are shown graphically: (1) Propagation characteristics of one-, two-, three- and four-soliton solutions are discussed from vanishing background. (2) Propagation characteristics of one- and two-breather solutions are analyzed from the plane wave background. The details of the dynamical evolutions for such soliton and breather solutions are studied via numerical simulations. Numerical results show the accuracy of our numerical scheme and the stable evolutions of these solitons with or without a noise in a relatively short period of time, while the evolutions exhibit obviously larger oscillations and strong instability with the increase in time. These results may be useful for understanding the propagation of orthogonally polarized optical waves in an isotropic medium and circularly polarized few-cycle pulses in Kerr media described by the coupled NLS and coupled complex mKdV equations, respectively.

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DAI, CHAO-QING y JIE-FANG ZHANG. "TRAVELLING WAVE SOLUTIONS TO THE COUPLED DISCRETE NONLINEAR SCHRÖDINGER EQUATIONS". International Journal of Modern Physics B 19, n.º 13 (20 de mayo de 2005): 2129–43. http://dx.doi.org/10.1142/s0217979205029778.

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In this paper, we have utilized the extended Jacobian elliptic function approach to construct seven families of new Jacobian elliptic function solutions for the coupled discrete nonlinear Schrödinger equations. When the modulus m → 1 or 0, some of these obtained solutions degenerate to the soliton solutions (the moving bright-bright and dark-dark solitons), the solitonic solutions and the trigonometric function solutions. This integrable model possesses the moving solitons because there is no PN barrier to block their motion in the lattice. We also find that some solutions in differential-difference equations (DDEs) are essentially identical to the continuous cases, while some solutions such as sec-type and tan-type in differential-difference models present different properties.

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GAO, JIE, HAI LI, JIANXIONG WU, LINGYAN LI, ZHIJIE MAI y GUIHUA CHEN. "ELECTROMAGNETICALLY INDUCED QUANTUM LATTICE SOLITON". Journal of Nonlinear Optical Physics & Materials 21, n.º 01 (marzo de 2012): 1250011. http://dx.doi.org/10.1142/s0218863512500117.

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An optical atomic discrete system through optical induction is proposed. A theoretical scheme to produce quantum discrete or lattice solitons (QLSs) in the system is presented with the use of the effects of enhanced self-phase modulation and cross-phase modulation through the giant kerr effect in the electromagnetically induced transparency. The power density and the photon flux can be tuned to a very low level by the coupling field and the soliton can propagate with very slow group velocity.

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Wael Sulayman Miftah Ammar y Ying Shi. "The application of the KdV type equation in engineering simulation". Maejo International Journal of Energy and Environmental Communication 3, n.º 2 (4 de junio de 2021): 7–10. http://dx.doi.org/10.54279/mijeec.v3i2.245174.

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Bores propagating in shallow water transform into undular bores and, finally, into trains of solitons. The observed number and height of these undulations and later discrete solitons are strongly dependent on the propagation length of the bore. Empirical results show that the final height of the leading soliton in the far-field is twice the initial mean bore height. The complete disintegration of the initial bore into a train of solitons requires very long propagation, but unfortunately, these required distances are usually not available in experimental tests of nature. Therefore, the analysis of the bore decomposition for experimental data into solitons is complicated and requires different approaches. Previous studies have shown that by applying the nonlinear Fourier transform based on the Ko- rteweg–de Vries equation (KdV-NFT) to bores and long-period waves propagating in constant depth, the number and height of all solitons can be reliably predicted already based on the initial bore-shaped free surface. Against this background, this study presents the systematic analysis of the leading-soliton amplitudes for non-breaking and breaking bores with different strengths in different water depths to validate the KdV-NFT results for non-breaking bores to show the limitations of wave breaking on the spectral results. The analytical results are compared with data from experimental tests, numerical simulations and other approaches from the literature.

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Eisenberg, H. S., R. Morandotti, Y. Silberberg, J. M. Arnold, G. Pennelli y J. S. Aitchison. "Optical discrete solitons in waveguide arrays I Soliton formation". Journal of the Optical Society of America B 19, n.º 12 (2 de diciembre de 2002): 2938. http://dx.doi.org/10.1364/josab.19.002938.

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ROSU, HARET C. "KdV ADIABATIC INDEX SOLITONS IN BAROTROPIC OPEN FRW COSMOLOGIES". Modern Physics Letters A 17, n.º 11 (10 de abril de 2002): 667–70. http://dx.doi.org/10.1142/s0217732302006898.

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Applying standard mathematical methods, it is explicitly shown how the Riccati equation for the Hubble parameter H (η) of barotropic open FRW cosmologies is connected with a Korteweg-de Vries equation for adiabatic index solitons. It is also shown how one can embed a discrete sequence of adiabatic indices of the type [Formula: see text], (γ ≠ 2/3), in the sech FRW adiabatic index soliton.

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Al-Amin, M., M. Nurul Islam, Onur Alp İlhan, M. Ali Akbar y Danyal Soybaş. "Solitary Wave Solutions to the Modified Zakharov–Kuznetsov and the (2 + 1)-Dimensional Calogero–Bogoyavlenskii–Schiff Models in Mathematical Physics". Journal of Mathematics 2022 (31 de octubre de 2022): 1–16. http://dx.doi.org/10.1155/2022/5224289.

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The modified Zakharov–Kuznetsov (mZK) and the (2 + 1)-dimensional Calogero–Bogoyavlenskii–Schiff (CBS) models convey a significant role to instruct the internal structure of tangible composite phenomena in the domain of two-dimensional discrete electrical lattice, plasma physics, wave behaviors of deep oceans, nonlinear optics, etc. In this article, the dynamic, companionable, and further broad-spectrum exact solitary solitons are extracted to the formerly stated nonlinear models by the aid of the recently enhanced auxiliary equation method through the traveling wave transformation. The implication of the soliton solutions attained with arbitrary constants can be substantial to interpret the involuted phenomena. The established soliton solutions show that the approach is broad-spectrum, efficient, and algebraic computing friendly and it may be used to classify a variety of wave shapes. We analyze the achieved solitons by sketching figures for distinct values of the associated parameters by the aid of the Wolfram Mathematica program.

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Hennig, Dirk, Nikos I. Karachalios y Jesús Cuevas-Maraver. "The closeness of localized structures between the Ablowitz–Ladik lattice and discrete nonlinear Schrödinger equations: Generalized AL and DNLS systems". Journal of Mathematical Physics 63, n.º 4 (1 de abril de 2022): 042701. http://dx.doi.org/10.1063/5.0072391.

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The Ablowitz–Ladik system, being one of the few integrable nonlinear lattices, admits a wide class of analytical solutions, ranging from exact spatially localized solitons to rational solutions in the form of the spatiotemporally localized discrete Peregrine soliton. Proving a closeness result between the solutions of the Ablowitz–Ladik system and a wide class of Discrete Nonlinear Schrödinger systems in a sense of a continuous dependence on their initial data, we establish that such small amplitude waveforms may be supported in nonintegrable lattices for significantly large times. Nonintegrable systems exhibiting such behavior include a generalization of the Ablowitz–Ladik system with power-law nonlinearity and the discrete nonlinear Schrödinger equation with power-law and saturable nonlinearities. The outcome of numerical simulations illustrates, in excellent agreement with the analytical results, the persistence of small amplitude Ablowitz–Ladik analytical solutions in all the nonintegrable systems considered in this work, with the most striking example being that of the Peregine soliton.

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Kirikchi, Omar B., Alhaji A. Bachtiar y Hadi Susanto. "Bright Solitons in aPT-Symmetric Chain of Dimers". Advances in Mathematical Physics 2016 (2016): 1–12. http://dx.doi.org/10.1155/2016/9514230.

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We study the existence and stability of fundamental bright discrete solitons in a parity-time- (PT-) symmetric coupler composed by a chain of dimers that is modelled by linearly coupled discrete nonlinear Schrödinger equations with gain and loss terms. We use a perturbation theory for small coupling between the lattices to perform the analysis, which is then confirmed by numerical calculations. Such analysis is based on the concept of the so-called anticontinuum limit approach. We consider the fundamental onsite and intersite bright solitons. Each solution has symmetric and antisymmetric configurations between the arms. The stability of the solutions is then determined by solving the corresponding eigenvalue problem. We obtain that both symmetric and antisymmetric onsite mode can be stable for small coupling, in contrast to the reported continuum limit where the antisymmetric solutions are always unstable. The instability is either due to the internal modes crossing the origin or the appearance of a quartet of complex eigenvalues. In general, the gain-loss term can be considered parasitic as it reduces the stability region of the onsite solitons. Additionally, we analyse the dynamic behaviour of the onsite and intersite solitons when unstable, where typically it is either in the form of travelling solitons or soliton blow-ups.

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Inc, Mustafa, Ahmed Elhassanein, Mohamed Aly Mohamed Abdou y Yu-Ming Chu. "On solitary wave solutions of a peptide group system with higher order saturable nonlinearity". Open Physics 18, n.º 1 (10 de diciembre de 2020): 933–38. http://dx.doi.org/10.1515/phys-2020-0201.

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Abstract In this article, a new continuous model of a peptide group system with higher order saturable nonlinearity is derived. The model is constructed up on discrete Schrodinger equation with higher order saturable nonlinearity. New exact solutions of the proposed model are investigated. Via the generalized Riccati equation mapping method travelling wave and soliton solutions are derived. For certain values of parameters kink, antikink, breathers, and dark and bright solitons are presented.

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Wang, Peiyao, Shangwen Peng, Yihao Cao y Rongpei Zhang. "The Conservative and Efficient Numerical Method of 2-D and 3-D Fractional Nonlinear Schrödinger Equation Using Fast Cosine Transform". Mathematics 12, n.º 7 (7 de abril de 2024): 1110. http://dx.doi.org/10.3390/math12071110.

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This paper introduces a novel approach employing the fast cosine transform to tackle the 2-D and 3-D fractional nonlinear Schrödinger equation (fNLSE). The fractional Laplace operator under homogeneous Neumann boundary conditions is first defined through spectral decomposition. The difference matrix Laplace operator is developed by the second-order central finite difference method. Then, we diagonalize the difference matrix based on the properties of Kronecker products. The time discretization employs the Crank–Nicolson method. The conservation of mass and energy is proved for the fully discrete scheme. The advantage of this method is the implementation of the Fast Discrete Cosine Transform (FDCT), which significantly improves computational efficiency. Finally, the accuracy and effectiveness of the method are verified through two-dimensional and three-dimensional numerical experiments, solitons in different dimensions are simulated, and the influence of fractional order on soliton evolution is obtained; that is, the smaller the alpha, the lower the soliton evolution.

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Martynov, V. O., V. O. Munyaev y L. A. Smirnov. "Generation of entangled states of light using discrete solitons in waveguide arrays". Laser Physics Letters 19, n.º 5 (7 de abril de 2022): 055209. http://dx.doi.org/10.1088/1612-202x/ac624e.

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Abstract We study the quantum properties of light propagating through an array of coupled nonlinear waveguides and forming a discrete soliton. We demonstrate that it is possible to use certain types of quasi-solitons to form continuous variables entanglement between the certain pair of waveguides. Moreover, there is a possibility to entangle several pairs of waveguides independently. We show that the entanglement is generated for arbitrary high intensity of the input laser field, so it does not require a special material with an extremely high nonlinearity coefficient. Also, absorption in the waveguide media does not influence the discussed process too much.

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Cheng, Xu, Ernani Ribeiro y Detang Zhou. "On Euler characteristic and Hitchin-Thorpe inequality for four-dimensional compact Ricci solitons". Proceedings of the American Mathematical Society, Series B 10, n.º 3 (27 de febrero de 2023): 33–45. http://dx.doi.org/10.1090/bproc/155.

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In this article, we investigate the geometry of 4 4 -dimensional compact gradient Ricci solitons. We prove that, under an upper bound condition on the range of the potential function, a 4 4 -dimensional compact gradient Ricci soliton must satisfy the classical Hitchin-Thorpe inequality. In addition, some volume estimates are also obtained.

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Sarai, Akinori. "Self-consistent evaluation of static solitons, pinning energy and soliton energy in discrete one-dimensional soliton models". Physics Letters A 114, n.º 8-9 (marzo de 1986): 477–81. http://dx.doi.org/10.1016/0375-9601(86)90698-5.

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Aminikhah, H. y P. Dehghan. "Generalized Differential Transform Method for Solving Discrete Complex Cubic Ginzburg–Landau Equation". International Journal of Computational Methods 12, n.º 03 (junio de 2015): 1550017. http://dx.doi.org/10.1142/s0219876215500176.

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In this paper, generalized differential transform method (GDTM) is applied to solve discrete complex cubic Ginzburg–Landau (DCCGL) equation which is a famous nonlinear difference-differential equation (NDDE). GDTM approximate solutions for various discrete soliton solutions of DCCGL such as discrete bright soliton, discrete dark soliton, and discrete alternating soliton are obtained. Also this method is successfully employed to obtain approximate solution for dark solitary wave solution of integrable discrete nonlinear Schrödinger (IDNS) equation. Numerical results compared with their corresponding numerical and analytical solutions to show the efficiency and high accuracy of the considered method.

26

Doikou, Anastasia y Iain Findlay. "Solitons: Conservation laws and dressing methods". International Journal of Modern Physics A 34, n.º 06n07 (10 de marzo de 2019): 1930003. http://dx.doi.org/10.1142/s0217751x19300035.

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We review some of the fundamental notions associated with the theory of solitons. More precisely, we focus on the issue of conservation laws via the existence of the Lax pair and also on methods that provide solutions to partial or ordinary differential equations that are associated to discrete or continuous integrable systems. The Riccati equation associated to a given continuous integrable system is also solved and hence suitable conserved quantities are derived. The notion of the Darboux–Bäcklund transformation is introduced and employed in order to obtain soliton solutions for specific examples of integrable equations. The Zakharov–Shabat dressing scheme and the Gelfand–Levitan–Marchenko equation are also introduced. Via this method, generic solutions are produced and integrable hierarchies are explicitly derived. Various discrete and continuous integrable models are employed as examples such as the Toda chain, the discrete nonlinear Schrödinger model, the Korteweg–de Vries and nonlinear Schrödinger equations as well as the sine-Gordon and Liouville models.

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Li, Li. "A Higher-Dimensional Lie Algebra and 4×4 Discrete Soliton Hierarchy with Self-Consistent Sources". Advanced Materials Research 1061-1062 (diciembre de 2014): 1051–54. http://dx.doi.org/10.4028/www.scientific.net/amr.1061-1062.1051.

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In this paper, we aim to construct a super integrable discrete soliton hierarchy with self-consistent sources. A new isospectral problem is firstly presented, and we consider a discrete soliton hierarchy with self-consistent sources by using Lie algebra . Then, a new higher dimensional super integrable discrete soliton hierarchy with self-consistent sources is obtained. The method can be generalized to other soliton hierarchy with self-consistent sources.

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Xia, Yinhua y Yan Xu. "A Conservative Local Discontinuous Galerkin Method for the Schrödinger-KdV System". Communications in Computational Physics 15, n.º 4 (abril de 2014): 1091–107. http://dx.doi.org/10.4208/cicp.140313.160813s.

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AbstractIn this paper we develop a conservative local discontinuous Galerkin (LDG) method for the Schrödinger-Korteweg-de Vries (Sch-KdV) system, which arises in various physical contexts as a model for the interaction of long and short nonlinear waves. Conservative quantities in the discrete version of the number of plasmons, energy of the oscillations and the number of particles are proved for the LDG scheme of the Sch-KdV system. Semi-implicit time discretization is adopted to relax the time step constraint from the high order spatial derivatives. Numerical results for accuracy tests of stationary traveling soliton, and the collision of solitons are shown. Numerical experiments illustrate the accuracy and capability of the method.

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Lin, Zhe, Xiao-Yong Wen y Meng-Li Qin. "Various Soliton Solutions and Asymptotic State Analysis for the Discrete Modified Korteweg-de Vries Equation". Advances in Mathematical Physics 2021 (6 de octubre de 2021): 1–22. http://dx.doi.org/10.1155/2021/3445894.

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Under investigation is the discrete modified Korteweg-de Vries (mKdV) equation, which is an integrable discretization of the continuous mKdV equation that can describe some physical phenomena such as dynamics of anharmonic lattices, solitary waves in dusty plasmas, and fluctuations in nonlinear optics. Through constructing the discrete generalized m , N − m -fold Darboux transformation for this discrete system, the various discrete soliton solutions such as the usual soliton, rational soliton, and their mixed soliton solutions are derived. The elastic interaction phenomena and physical characteristics are discussed and illustrated graphically. The limit states of diverse soliton solutions are analyzed via the asymptotic analysis technique. Numerical simulations are used to display the dynamical behaviors of some soliton solutions. The results given in this paper might be helpful for better understanding the physical phenomena in plasma and nonlinear optics.

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Li, Li. "A New 3×3 Discrete Soliton Hierarchy with Self-Consistent Sources". Advanced Materials Research 1061-1062 (diciembre de 2014): 1055–58. http://dx.doi.org/10.4028/www.scientific.net/amr.1061-1062.1055.

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In this paper, we consider a discrete soliton hierarchy with self-consistent sources by using higher-dimensional matrix spectral problem. Then a new discrete soliton hierarchy with self-consistent sources is obtained.

31

Lederer, Falk y Yaron Silberberg. "Discrete Solitons". Optics and Photonics News 13, n.º 2 (1 de febrero de 2002): 48. http://dx.doi.org/10.1364/opn.13.2.000048.

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32

Dong, Huanhe, Xiaoqian Huang, Yong Zhang, Mingshuo Liu y Yong Fang. "The Darboux Transformation and N-Soliton Solutions of Gerdjikov–Ivanov Equation on a Time–Space Scale". Axioms 10, n.º 4 (5 de noviembre de 2021): 294. http://dx.doi.org/10.3390/axioms10040294.

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The Gerdjikov–Ivanov (GI) equation is one type of derivative nonlinear Schrödinger equation used widely in quantum field theory, nonlinear optics, weakly nonlinear dispersion water waves and other fields. In this paper, the coupled GI equation on a time–space scale is deduced from Lax pairs and the zero curvature equation on a time–space scale, which can be reduced to the classical and the semi-discrete GI equation by considering different time–space scales. Furthermore, the Darboux transformation (DT) of the GI equation on a time–space scale is constructed via a gauge transformation. Finally, N-soliton solutions of the GI equation are given through applying its DT, which are expressed by the Cayley exponential function. At the same time, one-solition solutions are obtained on three different time–space scales ( X = R, X = C and X = Kp ).

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Zhu, Jin-Yan y Yong Chen. "Long-time asymptotic behavior of the coupled dispersive AB system in low regularity spaces". Journal of Mathematical Physics 63, n.º 11 (1 de noviembre de 2022): 113504. http://dx.doi.org/10.1063/5.0102264.

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In this paper, we mainly investigate the long-time asymptotic behavior of the solution for coupled dispersive AB systems with weighted Sobolev initial data, which allows soliton solutions via the Dbar steepest descent method. Based on the spectral analysis of Lax pairs, the Cauchy problem of coupled dispersive AB systems is transformed into a Riemann–Hilbert problem, and the existence and uniqueness of its solution is proved by the vanishing lemma. The stationary phase points play an important role in determining the long-time asymptotic behavior of these solutions. We demonstrate that in any fixed time cone [Formula: see text], the long-time asymptotic behavior of the solution for coupled dispersive AB systems can be expressed by [Formula: see text] solitons on the discrete spectrum, the leading order term [Formula: see text] on the continuous spectrum, and the allowable residual [Formula: see text].

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Plath, P. J., J. K. Plath y J. Schwietering. "Collision patterns on mollusc shells". Discrete Dynamics in Nature and Society 1, n.º 1 (1997): 57–76. http://dx.doi.org/10.1155/s1026022697000071.

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On mollusc shells one can find famous patterns. Some of them show a great resemblance to the soliton patterns in one-dimensional systems. Other look like Sierpinsky triangles or exhibit very irregular patterns. Meinhardt has shown that those patterns can be well described by reaction–diffusion systems [1]. However, such a description neglects the discrete character of the cell system at the growth front of the mollusc shell.We have therefore developed a one-dimensional cellular vector automaton model which takes into account the cellular behaviour of the system [2]. The state of the mathematical cell is defined by a vector with two components. We looked for the most simple transformation rules in order to develop quite different types of waves: classical waves, chemical waves and different types of solitons. Our attention was focussed on the properties of the system created through the collision of two waves.

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Zolotaryuk, Yaroslav, Peter L. Christiansen y Mario Salerno. "AC Driven Directed Motion of Solitary Waves". International Journal of Modern Physics B 17, n.º 22n24 (30 de septiembre de 2003): 4428–33. http://dx.doi.org/10.1142/s0217979203022568.

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We study the possibility of unidirectional motion of a topological soliton of a dissipative (continuous and discrete) Klein-Gordon equation driven by AC forces with certain broken symmetries and with zero mean. The role played by the temporal asymmetry of the system in establishing soliton DC motions which resemble usual soliton ratchets is emphasized. The dependence of the soliton velocity on the system parameters is studied.

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SWAMI, O. P., V. KUMAR y A. K. NAGAR. "BRIGHT SOLITONS IN A PARAMETRICALLY DRIVEN DISCRETE NONLINEAR SCHRODINGER EQUATION". International Journal of Modern Physics: Conference Series 22 (enero de 2013): 570–75. http://dx.doi.org/10.1142/s2010194513010684.

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In this paper, we consider a parametrically driven discrete nonlinear Schrödinger equation. Analytical and numerical calculations are performed to determine the existence and stability of fundamental bright discrete solitons admitted by discrete nonlinear Schrödinger equation. We show that a parametric driving can destabilizes onsite bright solitons and stabilizes intersite bright discrete solitons. Stability windows of all the fundamental solitons are presented and approximations to the onset of instability are derived using perturbation theory, with accompanying numerical results.

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Yuan, Cui-Lian y Xiao-Yong Wen. "Discrete nonlocal N-fold Darboux transformation and soliton solutions in a reverse space-time nonlocal nonlinear self-dual network equation". Modern Physics Letters B 35, n.º 19 (15 de junio de 2021): 2150314. http://dx.doi.org/10.1142/s0217984921503140.

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In this paper, we construct a discrete nonlocal integrable lattice hierarchy related to a reverse space-time nonlocal nonlinear self-dual network equation which may have the potential applications in designing nonlocal electrical circuits and understanding the propagation of electrical signals. By means of nonlocal version of [Formula: see text]-fold Darboux transformation (DT) technique, discrete multi-soliton solutions in determinant form are constructed for the reverse space-time nonlocal nonlinear self-dual network equation. Through the asymptotic and graphic analysis, unstable soliton structures of one-, two- and three-soliton solutions are discussed graphically. We observe that the single components in this nonlocal equation display instability while the combined potential terms with nonlocal [Formula: see text]-symmetry show stable soliton structures. It is shown that these nonlocal solutions are clearly different from those of its corresponding local equation. The results given in this paper may explain the soliton propagation in electrical signals.

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Zhang, Xiangyu, Jinglei Chai, Dezhao Ou y Yongyao Li. "Antisymmetry breaking of discrete dipole gap solitons induced by a phase-slip defect". Modern Physics Letters B 28, n.º 12 (19 de mayo de 2014): 1450097. http://dx.doi.org/10.1142/s0217984914500973.

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In this paper, we study the antisymmetry breaking of discrete dipole soliton induced by a phase-slip one-dimensional discrete lattice, which contains on-site self-repulsive nonlinearity. This system can be realized in waveguide arrays system in optics or Bose–Einstein condensate in optical lattice. Different from the symmetry breaking occurring in the ground-state, antisymmetry breaking occurs in the first excited state, which contains antisymmetry. For this system, stable antisymmetric dipole soliton and anti-asymmetric are found, the symmetry transition between them is supercritical type. It is found that, increasing the total norm of the soliton or decreasing the coupled strength of the defect waveguide can lead to the antisymmetry breaking. Such kind of symmetry breaking can lead to the change of the tendency of some characters of the soliton.

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Malomed, Boris A. "Discrete and Semi-Discrete Multidimensional Solitons and Vortices: Established Results and Novel Findings". Entropy 26, n.º 2 (2 de febrero de 2024): 137. http://dx.doi.org/10.3390/e26020137.

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This article presents a concise survey of basic discrete and semi-discrete nonlinear models, which produce two- and three-dimensional (2D and 3D) solitons, and a summary of the main theoretical and experimental results obtained for such solitons. The models are based on the discrete nonlinear Schrödinger (DNLS) equations and their generalizations, such as a system of discrete Gross–Pitaevskii (GP) equations with the Lee–Huang–Yang corrections, the 2D Salerno model (SM), DNLS equations with long-range dipole–dipole and quadrupole–quadrupole interactions, a system of coupled discrete equations for the second-harmonic generation with the quadratic (χ(2)) nonlinearity, a 2D DNLS equation with a superlattice modulation opening mini-gaps, a discretized NLS equation with rotation, a DNLS coupler and its PT-symmetric version, a system of DNLS equations for the spin–orbit-coupled (SOC) binary Bose–Einstein condensate, and others. The article presents a review of the basic species of multidimensional discrete modes, including fundamental (zero-vorticity) and vortex solitons, their bound states, gap solitons populating mini-gaps, symmetric and asymmetric solitons in the conservative and PT-symmetric couplers, cuspons in the 2D SM, discrete SOC solitons of the semi-vortex and mixed-mode types, 3D discrete skyrmions, and some others.

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Erofeev, V. I., D. A. Kolesov y A. V. Leonteva. "NONLINEAR LOCALIZED WAVE IN A METAMATERIAL, THE MATHEMATICAL MODEL OF WHICH IS OBTAINED BY THE METHOD OF ALTERNATIVE CONTINUALIZATION". Problems of Strength and Plasticity 84, n.º 2 (2022): 157–67. http://dx.doi.org/10.32326/1814-9146-2022-84-2-157-167.

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A metamaterial is defined as a class of substances with a complex internal structure and unique physical and mechanical properties. As a rule, such a material is a complex periodic system, in the nodes of which there are not material points, but bodies of small but finite sizes, which have internal degrees of freedom. To describe metamaterials, gradient continuums are often used, which are obtained by continuumizing the equations of motion of discrete lattices consisting of identical masses and springs of different stiffness. However, it should be noted that the gradient continuum model must be dynamically consistent, i.e. stable and providing a finite rate of energy transfer, while in most gradient models the group velocity of waves increases indefinitely with frequency. To achieve dynamic consistency of the gradient continuum model, the continuum method proposed by A.V. Metrikine and H. Askes, the essence of which is the assumption of a nonlocal connection between the displacements of the lattice nodes and the resulting continuum (the method of alternative continualization). In this paper, this method is generalized to the case of finite deformations and applied to obtain a nonlinear dynamically consistent model of a metamaterial (gradient elastic medium). Within the framework of the obtained model, the formation of spatially localized nonlinear waves, which are strain solitons and their periodic analogs, in gradient-elastic media is studied. The sign of the dimensionless parameter, which is the ratio of the nonlinear addition to the spring stiffness to its linear stiffness, affects the polarity of the soliton. For positive values of the parameter (hard nonlinearity), the soliton has a negative polarity. For negative values of the parameter (soft nonlinearity), the soliton has a positive polarity. The magnitude of the nonlinearity does not affect the speed of wave propagation and their width, but affects their amplitude.

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Yagasaki, Kazuyuki, Alan R. Champneys y Boris A. Malomed. "Discrete embedded solitons". Nonlinearity 18, n.º 6 (31 de agosto de 2005): 2591–613. http://dx.doi.org/10.1088/0951-7715/18/6/010.

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42

Peschel, U., O. Egorov y F. Lederer. "Discrete cavity solitons". Optics Letters 29, n.º 16 (13 de agosto de 2004): 1909. http://dx.doi.org/10.1364/ol.29.001909.

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43

Makris, Konstantinos G., Sergiy Suntsov, Demetrios N. Christodoulides, George I. Stegeman y Alain Hache. "Discrete surface solitons". Optics Letters 30, n.º 18 (15 de septiembre de 2005): 2466. http://dx.doi.org/10.1364/ol.30.002466.

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44

Leykam, Daniel y Anton S. Desyatnikov. "Discrete multivortex solitons". Optics Letters 36, n.º 24 (15 de diciembre de 2011): 4806. http://dx.doi.org/10.1364/ol.36.004806.

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45

XU, XI-XIANG y HONG-XIANG YANG. "A HIERARCHY OF LATTICE SOLITON EQUATIONS AND ITS HIGHER-ORDER SYMMETRY CONSTRAINT". International Journal of Modern Physics B 21, n.º 15 (10 de junio de 2007): 2679–95. http://dx.doi.org/10.1142/s021797920703720x.

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Starting from a discrete matrix spectral problem, a hierarchy of lattice soliton equations is derived through a discrete zero curvature representation. The Hamiltonian structures are established for the resulting hierarchy. Then the higher-order symmetry constraint for the resulting hierarchy is studied. It is shown that under the higher-order symmetry constraint, each lattice soliton equation in the resulting hierarchy can be factored by an integrable symplectic map and a finite-dimensional Liouville integrable Hamiltonian system.

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Liu, Nan, Xiao-Yong Wen y Yaqing Liu. "Fission and fusion interaction phenomena of the discrete kink multi-soliton solutions for the Chen–Lee–Liu lattice equation". Modern Physics Letters B 32, n.º 19 (9 de julio de 2018): 1850211. http://dx.doi.org/10.1142/s0217984918502111.

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Chen–Lee–Liu (CLL) lattice equation is an integrable discretization of the CLL equation which can be used to model the evolution of the self-steepening optical pulses without self-phase modulation. In this paper, the discrete N-fold Darboux transformation (DT) is used to derive the discrete kink multi-soliton solutions in terms of determinant for CLL lattice equation. Soliton fission and fusion interaction structures of such solutions are shown graphically. The details of their evolution are investigated by using numerical simulations, showing that a small noise with amplitude less than or equal to 0.01 produces a strong oscillation and instability of these kink soliton solutions. The discrete generalized perturbation [Formula: see text]-fold DT is constructed to express some rational solutions in terms of the determinants of CLL lattice equation by modifying the discrete N-fold DT. Infinitely many conservation laws for CLL lattice equation are constructed based on its Lax representation. Results in this paper might be helpful for understanding the propagation of optical pulses.

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Guo, Rui, Jiang-Yan Song, Hong-Tao Zhang y Feng-Hua Qi. "Soliton solutions, conservation laws and modulation instability for the discrete coupled modified Korteweg–de Vries equations". Modern Physics Letters B 32, n.º 14 (20 de mayo de 2018): 1850152. http://dx.doi.org/10.1142/s021798491850152x.

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In this paper, the discrete coupled modified Korteweg–de Vries equations are systematically investigated. Based on the Lax pair, N-fold discrete Darboux transformation, discrete soliton solutions, conservation laws and modulation instability are analyzed and presented.

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Cheng, Xu y Detang Zhou. "Eigenvalues of the drifted Laplacian on complete metric measure spaces". Communications in Contemporary Mathematics 19, n.º 01 (24 de noviembre de 2016): 1650001. http://dx.doi.org/10.1142/s0219199716500012.

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In this paper, first we study a complete smooth metric measure space [Formula: see text] with the ([Formula: see text])-Bakry–Émery Ricci curvature [Formula: see text] for some positive constant [Formula: see text]. It is known that the spectrum of the drifted Laplacian [Formula: see text] for [Formula: see text] is discrete and the first nonzero eigenvalue of [Formula: see text] has lower bound [Formula: see text]. We prove that if the lower bound [Formula: see text] is achieved with multiplicity [Formula: see text], then [Formula: see text], [Formula: see text] is isometric to [Formula: see text] for some complete [Formula: see text]-dimensional manifold [Formula: see text] and by passing an isometry, [Formula: see text] must split off a gradient shrinking Ricci soliton [Formula: see text], [Formula: see text]. This result can be applied to gradient shrinking Ricci solitons. Secondly, we study the drifted Laplacian [Formula: see text] for properly immersed self-shrinkers in the Euclidean space [Formula: see text], [Formula: see text] and show the discreteness of the spectrum of [Formula: see text] and a logarithmic Sobolev inequality.

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Nishinari, K. "A Discrete Model of an Extensible String in Three-Dimensional Space". Journal of Applied Mechanics 66, n.º 3 (1 de septiembre de 1999): 695–701. http://dx.doi.org/10.1115/1.2791597.

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In this paper, a discrete model of an extensible string in three-dimensional space is presented. The model contains the bending and twisting of a string, and becomes the special Cosserat string in the continuous limit. We also present a new method of analyzing a string in space by the soliton theory, which can reduce the basic equations to a simpler tractable form. Some exact solutions are obtained by the soliton theory. The discrete basic equations are also shown to be suitable for numerical simulations of string dynamics.

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SOBHY, MOHAMED I. y A. STUART BURMAN. "THE TRANSITION FROM SOLITONS TO CHAOS IN THE SOLUTION OF THE LOGISTIC EQUATION". International Journal of Bifurcation and Chaos 10, n.º 12 (diciembre de 2000): 2823–29. http://dx.doi.org/10.1142/s0218127400001821.

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The discrete logistic map was one of the first equations to be studied for the production of chaos. We shall show that a soliton solution exists for the differential logistic equation when the output is the derivative of the dependent variable rather than the variable itself. Furthermore, when the logistic equation is solved using Euler's forward algorithm a transition from a soliton solution to chaos exists and can be accurately predicted. The results are used directly to design an electronic soliton generator.

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