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Autor: Grafiati

Data publikacji: 4 czerwca 2021

Data aktualizacji: 18 lutego 2022

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1

Xu, Tao, Yong Chen i Zhijun Qiao. "Multi-dark soliton solutions for the (2+1)-dimensional multi-component Maccari system". Modern Physics Letters B 33, nr 31 (10.11.2019): 1950390. http://dx.doi.org/10.1142/s0217984919503901.

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Based on reduction of the KP hierarchy, the general multi-dark soliton solutions in Gram type determinant forms for the (2[Formula: see text]+[Formula: see text]1)-dimensional multi-component Maccari system are constructed. Especially, the two component coupled Maccari system comprising of two component short waves and single-component long waves are discussed in detail. Besides, the dynamics of one and two dark-dark solitons are analyzed. It is shown that the collisions of two dark-dark solitons are elastic by asymptotic analysis. Additionally, the two dark-dark solitons bound states are studied through two different cases (stationary and moving cases). The bound states can exist up to arbitrary order in the stationary case, however, only two-soliton bound state exists in the moving case. Besides, the oblique stationary bound state can be generated for all possible combinations of nonlinearity coefficients consisting of positive, negative and mixed cases. Nevertheless, the parallel stationary and the moving bound states are only possible when nonlinearity coefficients take opposite signs.

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2

VELARDE, MANUEL G., ALEXANDER P. CHETVERIKOV, WERNER EBELING, DIRK HENNIG i JOHN J. KOZAK. "ON THE MATHEMATICAL MODELING OF SOLITON-MEDIATED LONG-RANGE ELECTRON TRANSFER". International Journal of Bifurcation and Chaos 20, nr 01 (styczeń 2010): 185–94. http://dx.doi.org/10.1142/s0218127410025508.

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We discuss here possible models for long-range electron transfer (ET) between a donor (D) and an acceptor (A) along an anharmonic (Morse–Toda) one-dimensional (1d)-lattice. First, it is shown that the electron may form bound states (solectrons) with externally, mechanically excited solitons in the lattice thus leading to one form of soliton-mediated transport. These solectrons generally move with supersonic velocity. Then, in a thermally excited lattice, it is shown that solitons can also trap electrons, forming similar solectron bound states; here, we find that ET based on hopping can be modeled as a diffusion-like process involving not just one but several solitons. It is shown that either of these two soliton-assisted modes of transport can facilitate ET over quite long distances.

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3

Zhong, Hui, i Bo Tian. "Stochastic Soliton Solutions of the High-Order Nonlinear Schrödinger Equation in the Optical Fiber with Stochastic Dispersion and Nonlinearity". Zeitschrift für Naturforschung A 69, nr 1-2 (1.02.2014): 21–33. http://dx.doi.org/10.5560/zna.2013-0071.

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In this paper, the high-order nonlinear Schrödinger (HNLS) equation driven by the Gaussian white noise, which describes the wave propagation in the optical fiber with stochastic dispersion and nonlinearity, is studied. With the white noise functional approach and symbolic computation, stochastic one- and two-soliton solutions for the stochastic HNLS equation are obtained. For the stochastic one soliton, the energy and shape keep unchanged along the soliton propagation, but the velocity and phase shift change randomly because of the effects of Gaussian white noise. Ranges of the changes increase with the increase in the intensity of Gaussian white noise, and the direction of velocity is inverted along the soliton propagation. For the stochastic two solitons, the effects of Gaussian white noise on the interactions in the bound and unbound states are discussed: In the bound state, periodic oscillation of the two solitons is broken because of the existence of the Gaussian white noise, and the oscillation of stochastic two solitons forms randomly. In the unbound state, interaction of the stochastic two solitons happens twice because of the Gaussian white noise. With the increase in the intensity of Gaussian white noise, the region of the interaction enlarges.

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4

Yang, S. R. Eric. "Soliton Fractional Charges in Graphene Nanoribbon and Polyacetylene: Similarities and Differences". Nanomaterials 9, nr 6 (14.06.2019): 885. http://dx.doi.org/10.3390/nano9060885.

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An introductory overview of current research developments regarding solitons and fractional boundary charges in graphene nanoribbons is presented. Graphene nanoribbons and polyacetylene have chiral symmetry and share numerous similar properties, e.g., the bulk-edge correspondence between the Zak phase and the existence of edge states, along with the presence of chiral boundary states, which are important for charge fractionalization. In polyacetylene, a fermion mass potential in the Dirac equation produces an excitation gap, and a twist in this scalar potential produces a zero-energy chiral soliton. Similarly, in a gapful armchair graphene nanoribbon, a distortion in the chiral gauge field can produce soliton states. In polyacetylene, a soliton is bound to a domain wall connecting two different dimerized phases. In graphene nanoribbons, a domain-wall soliton connects two topological zigzag edges with different chiralities. However, such a soliton does not display spin-charge separation. The existence of a soliton in finite-length polyacetylene can induce formation of fractional charges on the opposite ends. In contrast, for gapful graphene nanoribbons, the antiferromagnetic coupling between the opposite zigzag edges induces integer boundary charges. The presence of disorder in graphene nanoribbons partly mitigates antiferromagnetic coupling effect. Hence, the average edge charge of gap states with energies within a small interval is e / 2 , with significant charge fluctuations. However, midgap states exhibit a well-defined charge fractionalization between the opposite zigzag edges in the weak-disorder regime. Numerous occupied soliton states in a disorder-free and doped zigzag graphene nanoribbon form a solitonic phase.

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5

Huang, Guoxiang, Zhupei Shi, Xianxi Dai i Ruibao Tao. "Two-Soliton Bound States in a Heisenberg Spin Chain". Communications in Theoretical Physics 16, nr 1 (lipiec 1991): 93–96. http://dx.doi.org/10.1088/0253-6102/16/1/93.

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6

MANTOVANI-SARTI, VALENTINA, BYUNG-YOON PARK i VICENTE VENTO. "THE SOLITON–SOLITON INTERACTION IN THE CHIRAL DILATON MODEL". International Journal of Modern Physics A 28, nr 27 (30.10.2013): 1350136. http://dx.doi.org/10.1142/s0217751x13501364.

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We study the interaction between two B = 1 states in the Chiral Dilaton Model where baryons are described as nontopological solitons arising from the interaction of chiral mesons and quarks. By using the hedgehog solution for B = 1 states we construct, via a product ansatz, three possible B = 2 configurations to analyse the role of the relative orientation of the hedgehog quills in the dynamics of the soliton–soliton interaction and investigate the behavior of these solutions in the range of long/intermediate distance. One of the solutions is quite binding due to the dynamics of the π and σ fields at intermediate distance and should be used for nuclear matter studies. Since the product ansatz break down as the two solitons get close, we explore the short range distance regime with a model that describes the interaction via a six-quark bag ansatz. We calculate the interaction energy as a function of the inter-soliton distance and show that for small separations the six quarks bag, assuming a hedgehog structure, provides a stable bound state that at large separations connects with a special configuration coming from the product ansatz.

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7

Chai, Jun, Bo Tian, Yu-Feng Wang, Wen-Rong Sun i Yun-Po Wang. "Conservation Laws and Mixed-Type Vector Solitons for the 3-Coupled Variable-Coefficient Nonlinear Schrödinger Equations in Inhomogeneous Multicomponent Optical Fibre". Zeitschrift für Naturforschung A 71, nr 6 (1.06.2016): 525–39. http://dx.doi.org/10.1515/zna-2016-0019.

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AbstractIn this article, the propagation and collision of vector solitons are investigated from the 3-coupled variable-coefficient nonlinear Schrödinger equations, which describe the amplification or attenuation of the picosecond pulses in the inhomogeneous multicomponent optical fibre with different frequencies or polarizations. On the basis of the Lax pair, infinitely-many conservation laws are obtained. Under an integrability constraint among the variable coefficients for the group velocity dispersion (GVD), nonlinearity and fibre gain/loss, and two mixed-type (2-bright-1-dark and 1-bright-2-dark) vector one- and two-soliton solutions are derived via the Hirota method and symbolic computation. Influence of the variable coefficients for the GVD and nonlinearity on the vector soliton amplitudes and velocities is analysed. Through the asymptotic and graphic analysis, bound states and elastic and inelastic collisions between the vector two solitons are investigated: Not only the elastic but also inelastic collision between the 2-bright-1-dark vector two solitons can occur, whereas the collision between the 1-bright-2-dark vector two solitons is always elastic; for the bound states, the GVD and nonlinearity affect their types; with the GVD and nonlinearity being the constants, collision period decreases as the GVD increases but is independent of the nonlinearity.

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8

Wang, Guomei, Guangwei Chen, Wenlei Li, Chao Zeng i Wei Zhao. "Observation of evolution dynamics from bound states to single-pulse states in a passively mode-locked fiber laser". Modern Physics Letters B 33, nr 09 (30.03.2019): 1950103. http://dx.doi.org/10.1142/s0217984919501033.

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We report what is, to our knowledge, the first experimental observation of the ultrafast evolution dynamics from bound states (BSs) to single-pulse states (SPSs) by using the dispersive Fourier-transform (DFT) technique. The evolutions from three categories of initial BSs to SPSs are spectrally resolved in real time. Usually, accompanied by complex soliton–soliton interaction and competition, one of the two bound pulses weakens to disappearance, and the other one evolves into SPS. During the transition, the two bound pulses ordinarily depart away from each other with complex changes of relative phase. However, it is found that not all the evolutions are accompanied by the increase of temporal separation between two bound pulses. The obtained results would facilitate a deep understanding of complex dynamics in nonlinear systems and provide valuable data for further theoretical studies.

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9

Liu, Lei, Bo Tian, Xiao-Yu Wu i Yu-Qiang Yuan. "Vector Dark Solitons for a Coupled Nonlinear Schrödinger System with Variable Coefficients in an Inhomogeneous Optical Fibre". Zeitschrift für Naturforschung A 72, nr 8 (28.08.2017): 779–87. http://dx.doi.org/10.1515/zna-2017-0148.

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AbstractStudied in this paper are the vector dark solitons for a coupled nonlinear Schrödinger system with variable coefficients, which can be used to describe the pulse simultaneous propagation of the M-field components in an inhomogeneous optical fibre, where M is a positive integer. When M=2, under the integrable constraint, we construct the nondegenerate N-dark-dark soliton solutions in terms of the Gramian through the Kadomtsev–Petviashvili hierarchy reduction. With the help of analytic analysis, a vector one soliton with varying amplitude and velocity is studied. Interactions and bound states between the two solitons under different group velocity dispersion and amplification/absorption coefficients are presented. Moreover, we extend our analysis to any M to obtain the nondegenerate vector N-dark soliton solutions.

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10

Zhang, Liqiang, Zhiyong Pan, Zhuang Zhuo i Yunzheng Wang. "Three Multiple-Pulse Operation States of an All-Normal-Dispersion Dissipative Soliton Fiber Laser". International Journal of Optics 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/169379.

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Multiple-pulse operation states of an all-normal-dispersion Yb-doped double-clad dissipative soliton fiber laser are investigated in this paper. The proposed laser can deliver harmonic mode-locked pulses, bound states of dissipative solitons, and dual-wavelength dual-pulses. Stable second-harmonic and third-harmonic mode-locked pulse trains are obtained with the output power of 1.39 W and 1.46 W, respectively, and the corresponding single pulse energies are 12.1 nJ and 8.5 nJ. With the adjustment of pump power and the wave plates, the fiber laser generates bound states of two or three dissipative solitons. Moreover, a dual-wavelength dual-pulse state is presented, where the output pulses from the nonlinear polarization rotation rejection port consists of the leading and trailing edges of the pulses circulating in the cavity.

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11

Qadir, Muhammad Irfan, i Usama Tahir. "Bound states of atomic Josephson vortices". Canadian Journal of Physics 95, nr 4 (kwiecień 2017): 336–39. http://dx.doi.org/10.1139/cjp-2016-0599.

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We study the existence and stability of the bound state Josephson vortices solution in two parallel quasi one-dimensional coupled Bose–Einstein condensates. The system can be elucidated by linearly coupled Gross–Pitaevskii equations. The purpose of this study is to investigate the effects of altering the strength of coupling between the two condensates over the stability of the bound-state Josephson vortices. It is found that the stability of bound-state Josephson vortices depends on the value of coupling strength. However, at a critical value of coupling parameter, the Josephson vortices solution transforms into a coupled dark soliton.

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12

Burzlaff, J. "The soliton number of optical soliton bound states for two special families of input pulses". Journal of Physics A: Mathematical and General 21, nr 2 (21.01.1988): 561–66. http://dx.doi.org/10.1088/0305-4470/21/2/034.

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13

GANDENBERGER, GEORG M. "TRIGONOMETRIC S MATRICES, AFFINE TODA SOLITONS AND SUPERSYMMETRY". International Journal of Modern Physics A 13, nr 26 (20.10.1998): 4553–90. http://dx.doi.org/10.1142/s0217751x98002195.

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Using [Formula: see text]- and [Formula: see text]-invariant R matrices we construct exact S matrices in two-dimensional space–time. These are conjectured to describe the scattering of solitons in affine Toda field theories. In order to find the spectrum of soliton bound states we examine the pole structure of these S matrices in detail. We also construct the S matrices for all scattering processes involving scalar bound states. In the last part of this paper we discuss the connection of these S matrices with minimal N=1 and N = 2 super-symmetric S matrices. In particular we comment on the folding from N = 2 to N = 1 theories.

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14

Dmitriev, Sergey V., i Takeshi Shigenari. "Short-lived two-soliton bound states in weakly perturbed nonlinear Schrödinger equation". Chaos: An Interdisciplinary Journal of Nonlinear Science 12, nr 2 (czerwiec 2002): 324–31. http://dx.doi.org/10.1063/1.1476951.

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15

Shao, Li, Yun-Long Wu i Qing Ye. "Anomalous Propagation Characteristics of Airy Beam in Nonlinear Kerr Media". Crystals 11, nr 8 (28.07.2021): 879. http://dx.doi.org/10.3390/cryst11080879.

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The propagation characteristics of a single Airy beam in nonlinear Kerr media were numerically investigated by utilizing the split-step Fourier transform method. We show that in addition to normal breathing solitons, the anomalous bound states of Airy spatial solitons can also be formed, which are similar to the states formed in the interaction between two Airy beams in nonlinear media. This quasi-equilibrium state is formed by the interaction of the main soliton beam and side lobes of Airy beam due to their different propagation trajectories in the nonlinear media. Moreover, it has been shown the Airy spatial solitons in tree structure can be formed by adjusting the initial parameters in the interaction between the Airy beam and Kerr media.

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16

Ren, Bo. "Characteristics of the Soliton Molecule and Lump Solution in the 2 + 1 -Dimensional Higher-Order Boussinesq Equation". Advances in Mathematical Physics 2021 (9.04.2021): 1–7. http://dx.doi.org/10.1155/2021/5545984.

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The soliton molecules, as bound states of solitons, have attracted considerable attention in several areas. In this paper, the 2 + 1 -dimensional higher-order Boussinesq equation is constructed by introducing two high-order Hirota operators in the usual 2 + 1 -dimensional Boussinesq equation. By the velocity resonance mechanism, the soliton molecule and the asymmetric soliton of the higher-order Boussinesq equation are constructed. The soliton molecule does not exist for the usual 2 + 1 -dimensional Boussinesq equation. As a special kind of rational solution, the lump wave is localized in all directions and decays algebraically. The lump solution of the higher-order Boussinesq equation is obtained by using a quadratic function. This lump wave is just the bright form by some detail analysis. The graphics in this study are carried out by selecting appropriate parameters. The results in this work may enrich the variety of the dynamics of the high-dimensional nonlinear wave field.

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17

Feng, Yu-Jie, Yi-Tian Gao, Ting-Ting Jia i Liu-Qing Li. "Soliton interactions of a variable-coefficient three-component AB system for the geophysical flows". Modern Physics Letters B 33, nr 29 (20.10.2019): 1950354. http://dx.doi.org/10.1142/s0217984919503548.

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Geophysical flows consist of the large-scale motions of the ocean and/or atmosphere. Researches on the geophysical flows reveal the mechanisms for the transport and redistribution of energy and matter. Investigated in this paper is a variable-coefficient three-component AB system for the baroclinic instability processes in geophysical flows. With respect to the three wave packets as well as the correction to the mean flow, bilinear forms are obtained, and one-, two- and [Formula: see text]-soliton solutions are derived under some coefficient constraints via the Hirota method. Soliton interaction is graphically investigated: (1) Velocities of the [Formula: see text] and [Formula: see text] components and amplitude of the [Formula: see text] component are proportional to the parameter measuring the state of the basic flow, where [Formula: see text] is the [Formula: see text]th wave packet with [Formula: see text] and [Formula: see text] is related to the mean flow; Amplitudes of the [Formula: see text] components decrease with the group velocity increasing; Parabolic-type solitons, sine-type solitons and quasi-periodic-type two solitons are obtained; For the [Formula: see text] component, solitons with the varying amplitudes and dromion-like two solitons are shown; (2) Three types of the breathers with different interaction periods and numbers of the wave branches in a wave packet are analyzed; (3) Bound states are depicted; (4) Compression of the soliton is presented; (5) Interactions between/among the solitons and breathers are also illustrated.

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18

Qadir, Muhammad Irfan, i Tehseen Zoma. "Symmetric bound states of Josephson vortices in BEC". Canadian Journal of Physics 96, nr 2 (luty 2018): 208–12. http://dx.doi.org/10.1139/cjp-2017-0269.

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A system of two parallel coupled cigar-shaped Bose–Einstein condensates is considered in an effectively one-dimensional limit. The dynamics of the system is characterized by a pair of coupled nonlinear Gross–Pitaevskii equations. In particular, the existence and stability of symmetric bound states of Josephson vortices are investigated. It is realized that the symmetric bound state Josephson vortices solution persists stably in its whole domain of existence for the coupling strength. Nevertheless, the bound states solution converts into a dark soliton at a critical value of coupling parameter.

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19

ZHENG, WEIHONG, CHRIS J. HAMER, RAJIV R. P. SINGH, SIMON TREBST i HARTMUT MONIEN. "LINKED CLUSTER SERIES EXPANSIONS FOR TWO-PARTICLE STATES IN QUANTUM LATTICE MODELS". International Journal of Modern Physics B 17, nr 28 (10.11.2003): 5011–20. http://dx.doi.org/10.1142/s0217979203020144.

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We have developed strong-coupling series expansion methods to study the two-particle spectra in quantum lattice models. The properties of bound states and multiparticle excitations can reveal important information about the dynamics of a given model. At the heart of this method lies the calculation of an effective Hamiltonian in the two-particle subspace. We use an orthogonal transformation to perform this block diagonalising, and find that maintaining orthogonality is crucial for cases where the ground state and the two-particle subspace have identical quantum numbers. The two-particle Schrödinger equation is solved by using a finite lattice approach in coordinate space or an integral equation in momentum space. These methods allow us to determine precisely the low-lying excitation spectra and dispersion relations for the two-particle bound states. The method has been tested for the (1+1) D transverse Ising model, and applied to the two-leg spin-1/2 Heisenberg ladder. We study the coherence lengths of the bound states, and how they merge with the two-particle continuum. Finally, these techniques are applied to the frustrated alternating Heisenberg chain, which has been of considerable recent interest due to its relevance to spin-Peierls systems such as CuGeO 3. Starting from a limit corresponding to weakly-coupled dimers, we develop high-order series expansions for the effective Hamiltonian in the two-particle subspace. In the regime of strong dimerisation, various properties of the singlet and triplet bound states, and the quintet antibound states, can be accurately calculated. We also study the behaviour as the external bond alternation vanishes, and the way in which the bound states of triplet dimer excitations make the transition to a soliton-antisoliton continuum.

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20

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, nr 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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21

Li, Z. J., H. B. Xu i K. L. Yao. "The Energy Band Structure of Polyacene with Soliton Excitation". Modern Physics Letters B 11, nr 11 (10.05.1997): 477–83. http://dx.doi.org/10.1142/s021798499700058x.

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Starting from the extensional Su–Schrieffer–Heeger model taking into account the effects of interchain coupling, we have studied the energy spectra and electronic states of soliton excitation in polyacene. The dimerized displacement u0 is found to be similar to the case of trans-polyacetylene, and equals to 0.04 Å. The energy-band gap is 0.38 eV, in agreement with the results derived by other authors. Two new bound electronic states have been found in the conduction band and in the valence band, which is different from the one of trans-polyacetylene. There exists two degenerate soliton states in the center of energy gap. Furthermore, the distribution of charge density and spin density have been discussed in detail.

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22

Vakhnenko, V. O., i E. J. Parkes. "Approach in Theory of Nonlinear Evolution Equations: The Vakhnenko-Parkes Equation". Advances in Mathematical Physics 2016 (2016): 1–39. http://dx.doi.org/10.1155/2016/2916582.

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A variety of methods for examining the properties and solutions of nonlinear evolution equations are explored by using the Vakhnenko equation (VE) as an example. The VE, which arises in modelling the propagation of high-frequency waves in a relaxing medium, has periodic and solitary traveling wave solutions some of which are loop-like in nature. The VE can be written in an alternative form, known as the Vakhnenko-Parkes equation (VPE), by a change of independent variables. The VPE has anN-soliton solution which is discussed in detail. Individual solitons are hump-like in nature whereas the corresponding solution to the VE comprisesN-loop-like solitons. Aspects of the inverse scattering transform (IST) method, as applied originally to the KdV equation, are used to find one- and two-soliton solutions to the VPE even though the VPE’s spectral equation is third-order and not second-order. A Bäcklund transformation for the VPE is used to construct conservation laws. The standard IST method for third-order spectral problems is used to investigate solutions corresponding to bound states of the spectrum and to a continuous spectrum. This leads toN-soliton solutions andM-mode periodic solutions, respectively. Interactions between these types of solutions are investigated.

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23

GOBBI, CARLO, SIGFRIDO BOFFI i DMITRI E. KHARZEEV. "PRODUCTION OF CHARMONIUM-NUCLEON BOUND STATES IN THE TOPOLOGICAL SOLITON MODEL". Modern Physics Letters A 09, nr 32 (20.10.1994): 3035–40. http://dx.doi.org/10.1142/s0217732394002860.

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The photo- and electro-production cross-sections of charmonium-nucleon bound states on protons are calculated in the framework of the topological soliton model. The size of these cross-sections is predicted too small to be detected using present experimental facilities.

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24

He, Jun-Rong, i Lin Yi. "Formations of n-order two-soliton bound states in Bose–Einstein condensates with spatiotemporally modulated nonlinearities". Physics Letters A 378, nr 16-17 (marzec 2014): 1085–90. http://dx.doi.org/10.1016/j.physleta.2014.01.050.

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JÜRGENSEN, HELMUT, i PAULINE KRAAK. "SOLITON AUTOMATA BASED ON TREES". International Journal of Foundations of Computer Science 18, nr 06 (grudzień 2007): 1257–70. http://dx.doi.org/10.1142/s0129054107005303.

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Soliton automata are a mathematical model for molecular switching devices. For even the simple case of soliton automata based on trees the behaviour is not known. For example, only two examples of such soliton automata were known the transition monoid of which is not the symmetric group on the set of states; and in these cases the transition monoid is the corresponding alternating group. We establish new bounds on the number of states of a tree-based soliton automaton and a sufficient condition for when the transition monoid of such a soliton automaton consists only of even permutations of the set of states. We also summarize the results of a systematic enumeration of tree-based soliton automata by which additional exceptions were found, each an alternating group in its natural representation.

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26

Mahmood, M. F., W. W. Zachary i T. L. Gill. "Bound States of Envelope Solitons in Coupled Nonlinear Schrödinger Equations". Journal of Nonlinear Optical Physics & Materials 06, nr 01 (marzec 1997): 49–53. http://dx.doi.org/10.1142/s0218863597000046.

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Interaction of strongly and weakly overlapping solitons of two independent modes is analyzed in the framework of a system of coupled nonlinear Schrödinger equations with oscillating terms. A Hamiltonian formulation is employed. Our analysis reveals that the solitons form a strongly bound state with their centers coincident and weakly bound states with their centers separated from each other.

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27

Kevrekidis, P. G., B. A. Malomed i A. R. Bishop. "Bound states of two-dimensional solitons in the discrete nonlinear Schrödinger equation". Journal of Physics A: Mathematical and General 34, nr 45 (6.11.2001): 9615–29. http://dx.doi.org/10.1088/0305-4470/34/45/302.

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Akylas, T. R., Guenbo Hwang i Jianke Yang. "From non-local gap solitary waves to bound states in periodic media". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, nr 2137 (31.08.2011): 116–35. http://dx.doi.org/10.1098/rspa.2011.0341.

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Solitary waves in one-dimensional periodic media are discussed by employing the nonlinear Schrödinger equation with a spatially periodic potential as a model. This equation admits two families of gap solitons that bifurcate from the edges of Bloch bands in the linear wave spectrum. These fundamental solitons may be positioned only at specific locations relative to the potential; otherwise, they become non-local owing to the presence of growing tails of exponentially small amplitude with respect to the wave peak amplitude. Here, by matching the tails of such non-local solitary waves, high-order locally confined gap solitons, or bound states, are constructed. Details are worked out for bound states comprising two non-local solitary waves in the presence of a sinusoidal potential. A countable set of bound-state families, characterized by the separation distance of the two solitary waves, is found, and each family features three distinct solution branches that bifurcate near Bloch-band edges at small, but finite, amplitude. Power curves associated with these solution branches are computed asymptotically for large solitary-wave separation, and the theoretical predictions are consistent with numerical results.

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29

He, Y. J., Boris A. Malomed, Dumitru Mihalache, B. Liu, H. C. Huang, H. Yang i H. Z. Wang. "Bound states of one-, two-, and three-dimensional solitons in complex Ginzburg–Landau equations with a linear potential". Optics Letters 34, nr 19 (25.09.2009): 2976. http://dx.doi.org/10.1364/ol.34.002976.

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Yun, Ling. "Observations of bound states of two and three dissipative solitons in a figure-eight laser in a normal dispersion regime". Laser Physics 23, nr 4 (5.03.2013): 045106. http://dx.doi.org/10.1088/1054-660x/23/4/045106.

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LU DING-WEI, SUN XIN, FU ROU-LI i LIU JIE. "ELECTRONIC BOUND STATES OF CHARGED SOLITON". Acta Physica Sinica 39, nr 2 (1990): 289. http://dx.doi.org/10.7498/aps.39.289.

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Oh, Yongseok, i Byung-Yoon Park. "Energy levels of soliton–heavy-meson bound states". Physical Review D 51, nr 9 (1.05.1995): 5016–29. http://dx.doi.org/10.1103/physrevd.51.5016.

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Kockaert, P., i M. Haelterman. "Stability and symmetry breaking of soliton bound states". Journal of the Optical Society of America B 16, nr 5 (1.05.1999): 732. http://dx.doi.org/10.1364/josab.16.000732.

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Milián, C., D. E. Ceballos-Herrera, D. V. Skryabin i A. Ferrando. "Soliton-plasmon resonances as Maxwell nonlinear bound states". Optics Letters 37, nr 20 (5.10.2012): 4221. http://dx.doi.org/10.1364/ol.37.004221.

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Rho, Mannque, D. O. Riska i N. N. Scoccola. "Charmed baryons as soliton-D meson bound states". Physics Letters B 251, nr 4 (listopad 1990): 597–602. http://dx.doi.org/10.1016/0370-2693(90)90802-d.

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Bogdan, M. M., i O. V. Charkina. "Dynamics of bound soliton states in regularized dispersive equations". Low Temperature Physics 34, nr 7 (lipiec 2008): 564–70. http://dx.doi.org/10.1063/1.2957009.

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Latas, S. C. V., i M. F. S. Ferreira. "Self-frequency shift effect on dissipative soliton bound states". Applied Physics B 105, nr 4 (11.10.2011): 863–69. http://dx.doi.org/10.1007/s00340-011-4736-4.

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Kamburova, R. S., i M. T. Primatarowa. "Bound Soliton–Defect Spin States in Anisotropic Ferromagnetic Chains". Journal of Physics: Conference Series 1762, nr 1 (1.02.2021): 012020. http://dx.doi.org/10.1088/1742-6596/1762/1/012020.

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Kälbermann, G. "Decay to bound states of a soliton in a well". Chaos, Solitons & Fractals 12, nr 4 (3.01.2001): 625–29. http://dx.doi.org/10.1016/s0960-0779(00)00037-0.

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Latas, Sofia C. V., Mário F. S. Ferreira i Augusto S. Rodrigues. "Bound states of plain and composite pulses: Multi-soliton solutions". Optical Fiber Technology 11, nr 3 (lipiec 2005): 292–305. http://dx.doi.org/10.1016/j.yofte.2004.12.003.

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Afanasjev, V. V., i N. Akhmediev. "Soliton interaction and bound states in amplified-damped fiber systems". Optics Letters 20, nr 19 (1.10.1995): 1970. http://dx.doi.org/10.1364/ol.20.001970.

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Haelterman, M., S. Trillo i P. Ferro. "Multiple soliton bound states and symmetry breaking in quadratic media". Optics Letters 22, nr 2 (15.01.1997): 84. http://dx.doi.org/10.1364/ol.22.000084.

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Buryak, Alexander V. "Stationary soliton bound states existing in resonance with linear waves". Physical Review E 52, nr 1 (1.07.1995): 1156–63. http://dx.doi.org/10.1103/physreve.52.1156.

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Hołyst, J. A., i H. Benner. "Soliton-magnon bound states in TMMC above and below TN". Journal of Magnetism and Magnetic Materials 140-144 (luty 1995): 1969–70. http://dx.doi.org/10.1016/0304-8853(94)00717-9.

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Piette, Bernard, i Wojtek J. Zakrzewski. "Skyrmion model in 2 + 1 dimensions with soliton bound states". Nuclear Physics B 393, nr 1-2 (marzec 1993): 65–78. http://dx.doi.org/10.1016/0550-3213(93)90237-j.

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Basu-Mallick, B., Tanaya Bhattacharyya i Diptiman Sen. "Bound and anti-bound soliton states for a quantum integrable derivative nonlinear Schrödinger model". Physics Letters A 325, nr 5-6 (maj 2004): 375–80. http://dx.doi.org/10.1016/j.physleta.2004.04.010.

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Haelterman, M., i A. Sheppard. "Bifurcation phenomena and multiple soliton-bound states in isotropic Kerr media". Physical Review E 49, nr 4 (1.04.1994): 3376–81. http://dx.doi.org/10.1103/physreve.49.3376.

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Giachetti, R., i E. Sorace. "Two fermion relativistic bound states". Journal of Physics A: Mathematical and General 38, nr 6 (27.01.2005): 1345–70. http://dx.doi.org/10.1088/0305-4470/38/6/012.

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Britto-Pacumio, Ruth, Andrew Strominger i Anastasia Volovich. "Two-black-hole bound states". Journal of High Energy Physics 2001, nr 03 (29.03.2001): 050. http://dx.doi.org/10.1088/1126-6708/2001/03/050.

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Yennie, Donald R. "Two-body QED bound states". Zeitschrift für Physik C Particles and Fields 56, S1 (marzec 1992): S13—S23. http://dx.doi.org/10.1007/bf02426770.

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