A conservative numerical scheme for capturing interactions of optical solitons in a 2D coupled nonlinear Schrödinger system

Mousa, Mohamed M.; Ma, Wen‐Xiu

doi:10.1007/s12648-021-02065-6

Cited by 5 publications

(3 citation statements)

References 24 publications

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“…13 the trajectory and the 3D surface plots of this interaction are displayed for the soliton wave solution |u|, just for clarification. Recently, such interactions were examined in [31].…”

Section: Inelastic Interactions Of Two Solitons For Cnlsmentioning

confidence: 99%

Capturing of solitons collisions and reflections in nonlinear Schrödinger type equations by a conservative scheme based on MOL

et al. 2021

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In this work, we develop an efficient numerical scheme based on the method of lines (MOL) to investigate the interesting phenomenon of collisions and reflections of optical solitons. The established scheme is of second order in space and of fourth order in time with an explicit nature. We deduce stability restrictions using the von Neumann stability analysis. We consider a $(2+ 1)$ ( 2 + 1 ) -dimensional system of a coupled nonlinear Schrödinger equation as a general model of nonlinear Schrödinger-type equations. We consider several numerical experiments to demonstrate the robustness of the scheme in capturing many scenarios of collisions and reflections of the optical solitons related to nonlinear Schrödinger-type equations. We verify the scheme accuracy through computing the conserved invariants and comparing the present results with some existing ones in the literature.

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“…13 the trajectory and the 3D surface plots of this interaction are displayed for the soliton wave solution |u|, just for clarification. Recently, such interactions were examined in [31].…”

Section: Inelastic Interactions Of Two Solitons For Cnlsmentioning

confidence: 99%

Capturing of solitons collisions and reflections in nonlinear Schrödinger type equations by a conservative scheme based on MOL

et al. 2021

Self Cite

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“…In different researches, various integration techniques including, the new Jacobi elliptic function expansion method, the unified Riccati equation expansion method, and the new modified sub-ODE method, the modified Kudryashov method, sine-Gordon equation expansion method, and extended sinh-Gordon equation expansion method, the generalized Riccati equation mapping method and the ( ) ¢ G G -expansion method were used to infer unique solitary wave solutions of the NETL equation [9,11,16,25]. Several other prominent integration schemes have been also introduced and implemented in the recent past for analyzing the exact and approximated solutions of nonlinear equations, such as the modified extended auxiliary equation method, the fourth-order Runge-Kutta technique, nonlocal symmetry reductions technique, the exp(-f (ζ))-expansion, the extended Jacobian elliptic function expansion method and the adaptive moving mesh methods, Riccati-Bernoulli Sub-ODE approach, improvedexpansion approach, the generalized version of ( ) ¢ G G -expansion method, the Padés type transformation, sinecosine or triangle function approach, and several others [26][27][28][29][30][31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Construction of new traveling and solitary wave solutions of a nonlinear PDE characterizing the nonlinear low-pass electrical transmission lines

Kumar¹,

Kumar²,

Chand³

et al. 2021

Phys. Scr.

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In this study, we intend to analyze the traveling and several other solitary wave solutions in the nonlinear low-pass electrical transmission line model using the new mapping method, the new extended auxiliary equation method, and the extended Kudryashov method. A type of traveling and solitary wave solutions emerge, consisting of hyperbolic function, trigonometric, rational, periodic, and doubly periodic solutions that reflect kink, anti-kink wave solitons, bright-dark optical solitons, singular solitons, and other traveling waves. The three integration techniques applied are efficient, effective, and versatile for the creation of new bright, dark, singular, and non-singular periodic and solitary wave propagation solutions in nonlinear low-pass electrical transmission lines. To see the extant physical significance of the considered equation, we present some 2D and 3D figures for some solutions. We compare the obtained results with those obtained in the literature. We investigate and demonstrate the stability of the soliton solutions.

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“…Method of lines [12][13][14][15][16] as modified (G /G)-expansion method [17,18] is one of the efficient and accurate numerical methods that have been handled successfully to solve many partial differential equations (PDEs) with high accuracy. The idea of the MOL is summarized in reducing the given partial differential equations to a system of ordinary differential equations (ODEs) in the time by discretization of space variables and spatial derivatives using finite difference schemes.…”

Section: Introductionmentioning

confidence: 99%

A combined method for simulating MHD convection in square cavities through localized heating by method of line and penalty-artificial compressibility

Mousa

Ali

2021

Journal of Taibah University for Science

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A new combined technique is developed for studying free convection of magnetohydrodynamic unsteady incompressible flow in a square cavity that partially heated from lower wall and regular cooling from lateral walls. Convection has been studied for several lengths of heat source, Hartman and the Rayleigh numbers. The local and average Nusselt numbers are calculated and presented graphically along the heat source portion. The proposed technique is a combination of the method of lines (MOL) and a developed penalty-artificial compressibility technique (PACT). Unsteady penalty compressibility governing equations are used instead of solving steady-state balances. The penalty and artificial compressibility factors are estimated using a deduced stability restriction. The validation of the MOL-PACT is verified by comparing the current data with other numerical and experimental ones existing in the literature. The proposed technique provides a new choice through the investigation of MHD mass and heat transfer.

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A conservative numerical scheme for capturing interactions of optical solitons in a 2D coupled nonlinear Schrödinger system

Cited by 5 publications

References 24 publications

Capturing of solitons collisions and reflections in nonlinear Schrödinger type equations by a conservative scheme based on MOL

Capturing of solitons collisions and reflections in nonlinear Schrödinger type equations by a conservative scheme based on MOL

Construction of new traveling and solitary wave solutions of a nonlinear PDE characterizing the nonlinear low-pass electrical transmission lines

A combined method for simulating MHD convection in square cavities through localized heating by method of line and penalty-artificial compressibility

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