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Journal articles on the topic 'Singular Schrodinger equation'

Author: Grafiati

Published: 10 March 2023

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1

Troy, W. C. "New singular standing wave solutions of the nonlinear Schrodinger equation." Journal of Differential Equations 267, no. 2 (July 2019): 979–1000. http://dx.doi.org/10.1016/j.jde.2019.01.031.

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2

Zhunussova, Zh Kh. "The surface to singular solitonic solution of the nonlinear Schrodinger equation." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 88, no. 4 (December 30, 2017): 26–33. http://dx.doi.org/10.31489/2017m4/26-33.

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3

Tekercioglu, Ramazan. "On the traveling wave solutions of pulse propagation in monomode fiber via the extended Kudryashov’s approach." Thermal Science 26, Spec. issue 1 (2022): 49–59. http://dx.doi.org/10.2298/tsci22s1049t.

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In this research paper, we tackle with the solitary wave solutions to the pulse prop?agation in monomode optic fiber by defining non-linear Schrodinger equation with higher order. We applied the extended Kudryashov?s method with Bernoulli-Riccati equation and successfully gained soliton solutions and their contour, 2-D and 3-D graphical representations, such as dark, singular, periodic and kink type solutions. We also discussed the obtained results in the related section.

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4

Lin, Yuanhua, and Liping He. "Existence of Traveling Wave Fronts for a Generalized Nonlinear Schrodinger Equation." Advances in Mathematical Physics 2022 (August 16, 2022): 1–6. http://dx.doi.org/10.1155/2022/9638150.

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In the presented paper, a generalized nonlinear Schr o dinger equation without delay convolution kernel and with special delay convolution kernel is investigated. By using the geometric singular perturbation theory, the existence of traveling wave fronts is proved. Firstly, we show that such traveling wave fronts exist without delay by non-Hamiltonian qualitative analysis. Then, for the generalized nonlinear Schr o dinger equation with a special local strong delay convolution kernel, the desired heteroclinic orbit is obtained by using the Fredholm theory.

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5

Vshivteev, A. S., N. V. Norin, and V. N. Sorokin. "Spectral problem for the Schrodinger equation with singular potential polynomial of even degree." Russian Physics Journal 39, no. 5 (May 1996): 442–56. http://dx.doi.org/10.1007/bf02436783.

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6

ESTEVEZ, P. G., and G. A. HERNAEZ. "Painleve Analysis and Singular Manifold Method for a (2 + 1) Dimensional Non-Linear Schrodinger Equation." Journal of Non-linear Mathematical Physics 8, Supplement (2001): 106. http://dx.doi.org/10.2991/jnmp.2001.8.supplement.19.

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7

Kapitula, Todd. "Bifurcating bright and dark solitary waves for the perturbed cubic-quintic nonlinear Schrödinger equation." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 128, no. 3 (1998): 585–629. http://dx.doi.org/10.1017/s030821050002165x.

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The existence of bright and dark multi-bump solitary waves for Ginzburg–Landau type perturbations of the cubic-quintic Schrodinger equation is considered. The waves in question are not perturbations of known analytic solitary waves, but instead arise as a bifurcation from a heteroclinic cycle in a three-dimensional ODE phase space. Using geometric singular perturbation techniques, regions in parameter space for which 1-bump bright and dark solitary waves will bifurcate are identified. The existence of N-bump dark solitary waves (N ≧ 1) is shown via an application of the Exchange Lemma with Exponentially Small Error. N-bump bright solitary waves are shown to exist as a consequence of the work of Kapitula and Maier-Paape.

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8

Raza, Nauman, Riaz ur Rahman, Aly Seadawy, and Adil Jhangeer. "Computational and bright soliton solutions and sensitivity behavior of Camassa–Holm and nonlinear Schrödinger dynamical equation." International Journal of Modern Physics B 35, no. 11 (April 30, 2021): 2150157. http://dx.doi.org/10.1142/s0217979221501575.

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In this paper, we sketch and scrutinize the solitonic wave solution of Camassa–Holm equation by applying Kudryashov’s new method. We promote the algorithm of our new method to find the new solutions of this essential model. Camassa–Holm equation is a recent model in the point of distortion of hierarchies composition of integrability systems. It has been displayed that these solutions have the shape of dark, bright and singular solitons solutions of Camassa–Holm nonlinear Schrodinger equation. Graphically changing of extracted results of this model (CH) has been separated to grasp the substantial evolution. We analyze the sensitivity of the obtained solutions on behalf of different boundary conditions. It is fair that our model furnishes an impressive mathematical mechanism for manufacturing the solutions of the traveling wave for many models in physics and mathematics. The strategy utilized here is straightforward and succinct.

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9

Shalaby, A. M. "Dimensional Regularization of the Spatial wave function for a singular contact interaction in the Relativistic Schrodinger Equation." Journal of Physics: Conference Series 670 (January 25, 2016): 012045. http://dx.doi.org/10.1088/1742-6596/670/1/012045.

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10

CASAHORRÁN, J. "A NEW SUPERSYMMETRIC VERSION OF THE ABRAHAM-MOSES METHOD FOR SYMMETRIC POTENTIALS." Reviews in Mathematical Physics 08, no. 05 (July 1996): 655–68. http://dx.doi.org/10.1142/s0129055x96000226.

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Starting from the one-dimensional Schrodinger equation with symmetric potential Vs(x), a general method is presented in order to obtain a family of partially isospectral hamiltonians. Arguments concerning supersymmetric transformations, factorization procedures and Riccati equations are invoked along the article. As a result of the appearance of singular superpotentials, the physical meaning of our method can be summarized as follows: only the odd wave-functions of the original potential Vs(x) are transported via supersymmetry into the Hilbert space associated with the partner Vp(x). In such a case the degeneracy of energy levels is partially broken. Supersymmetry is neither exact nor spontaneously broken but realizes itself acting on wave functions vanishing at x=0. While the domain of the original hamiltonian H extends along the whole real axis, the susy partner Hp reduces to the half-line (x≤0 or x≥0). To illustrate how the procedure works in practice we resort to a symmetric potential in the Posch-Teller class containing both discrete and continuous spectra.

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11

Wang, Ming-Yue, Anjan Biswas, Yakup Yıldırım, Luminita Moraru, Simona Moldovanu, and Hashim M. Alshehri. "Optical Solitons for a Concatenation Model by Trial Equation Approach." Electronics 12, no. 1 (December 21, 2022): 19. http://dx.doi.org/10.3390/electronics12010019.

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This paper addresses the newly proposed concatenation model by the usage of trial equation approach. The concatenation is a chain model that is a combination of the nonlinear Schrodinger’s equation, Lakshmanan–Porsezian–Daniel model as well as the Sasa–Satsuma equation. The recovered solutions are displayed in terms of dark solitons, singular solitons, cnoidal waves and singular periodic waves. The trial equation approach enables to recover a wide spectrum of solutions to the governing model. The numerical schemes give a visual perspective to the solutions derived analytically.

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12

C., Moameni Abbas and Offin Daniel. "Positive Solutions for Singular Quasilinear Schrodinger Equations with One Parameter, II." Journal of Partial Differential Equations 23, no. 3 (June 2010): 222–34. http://dx.doi.org/10.4208/jpde.v23.n3.2.

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13

Javid, Ahmad, and Nauman Raza. "Chiral solitons of the (1 + 2)-dimensional nonlinear Schrodinger’s equation." Modern Physics Letters B 33, no. 32 (November 20, 2019): 1950401. http://dx.doi.org/10.1142/s0217984919504013.

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In this work, dark and singular soliton solutions of the (1[Formula: see text]+[Formula: see text]2)-dimensional chiral nonlinear Schrödinger’s equation are obtained and analyzed dynamically along with graphical depictions. The extraction of these chiral solitons is carried out using two integration tools such as the modified simple equation method and the [Formula: see text]-expansion method. The validity conditions for the existence of these solitons are also retrieved. It is highlighted that the solitons retrieved here are of chiral nature.

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14

Raza, Nauman, and Ahmad Javid. "Optical dark and dark-singular soliton solutions of (1+2)-dimensional chiral nonlinear Schrodinger’s equation." Waves in Random and Complex Media 29, no. 3 (April 3, 2018): 496–508. http://dx.doi.org/10.1080/17455030.2018.1451009.

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15

Gu, Yongyi, Jalil Manafian, Mustafa Z. Mahmoud, Sukaina Tuama Ghafel, and Onur Alp Ilhan. "New soliton waves and modulation instability analysis for a metamaterials model via the integration schemes." International Journal of Nonlinear Sciences and Numerical Simulation, October 13, 2022. http://dx.doi.org/10.1515/ijnsns-2021-0443.

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Abstract In this paper, the exact analytical solutions to the generalized Schrödinger equation are investigated. The Schrodinger type equations bearing nonlinearity are the important models that flourished with the wide-ranging arena concerning plasma physics, nonlinear optics, fluid-flow, and the theory of deep-water waves, etc. In this exploration, the soliton and other traveling wave solutions in an appropriate form to the generalized nonlinear Schrodinger equation by means of the extended sinh-Gordon equation expansion method, tan(Γ(ϖ))-expansion method, and the improved cos(Γ(ϖ)) function method are obtained. The suggested model of the nonlinear Schrodinger equation is turned into a differential ordinary equation of a single variable through executing some operations. One soliton, periodic, and singular wave solutions to this important equation in physics are reached. The periodic solutions are expressed in terms of the rational functions. Soliton solutions are obtained from them as a particular case. The obtained solutions are figured out in the profiles of 2D, density, and 3D plots by assigning suitable values of the involved unknown constants. Modulation instability (MI) is employed to discuss the stability of got solutions. These various graphical appearances enable the researchers to understand the underlying mechanisms of intricate phenomena of the leading equation. The individual performances of the employed methods are praiseworthy which deserves further application to unravel any other nonlinear partial differential equations (NLPDEs) arising in various branches of sciences. The proposed methodologies for resolving NLPDEs have been designed to be effectual, unpretentious, expedient, and manageable.

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16

Rehman, S. U., Aly R. Seadawy, M. Younis, S. T. R. Rizvi, T. A. Sulaiman, and A. Yusuf. "Modulation instability analysis and optical solitons of the generalized model for description of propagation pulses in optical fiber with four non-linear terms." Modern Physics Letters B, December 24, 2020, 2150112. http://dx.doi.org/10.1142/s0217984921501128.

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In this article, we investigate the optical soiltons and other solutions to Kudryashov’s equation (KE) that describe the propagation of pulses in optical fibers with four non-linear terms. Non-linear Schrodinger equation with a non-linearity depending on an arbitrary power is the base of this equation. Different kinds of solutions like optical dark, bright, singular soliton solutions, hyperbolic, rational, trigonometric function, as well as Jacobi elliptic function (JEF) solutions are obtained. The strategy that is used to extract the dynamics of soliton is known as [Formula: see text]-model expansion method. Singular periodic wave solutions are recovered and the constraint conditions, which provide the guarantee to the soliton solutions are also reported. Moreover, modulation instability (MI) analysis of the governing equation is also discussed. By selecting the appropriate choices of the parameters, 3D, 2D, and contour graphs and gain spectrum for the MI analysis are sketched. The obtained outcomes show that the applied method is concise, direct, elementary, and can be imposed in more complex phenomena with the assistant of symbolic computations.

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