(6)Solitary wave solutions for the variable-coefficient coupled nonlinear Schrödinger equations and Davey–Stewartson system using modified sine-Gordon equation method
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Rehab M. El-Shiekha,c,∗, Mahmoud Gaballahb
a Department of Mathematics,College of Science and Humanities at Howtat Sudair, Majmaah University, 11952, Saudi Arabia
b Department of Physics, College of Science at Al-Zulfi, Majmaah University, 11952, Saudi Arabia
c Department of Mathematics, Faculty of Education, Ain Shams University, Cairo, Egypt
Received 29 July 2019; received in revised form 29 October 2019; accepted 29 October 2019
Available online 19 November 2019
Abstract
In this study, the sine-Gordon equation method is modified to deal with variable-coefficient systems containing imaginary parts, such as
nonlinear Schrödinger systems. These are of considerable importance in many fields of research, including ocean engineering and optics. As
an example, we apply the modified method to variable-coefficient coupled nonlinear Schrö dinger equations and Davey–Stewartson system
with variable coefficients, treating them as one-dimensional and two-dimensional systems, respectively. As a result of this application, novel
solitary wave solutions are obtained for both cases. Moreover, some figures are provided to illustrate how the solitary wave propagation is
determined by the different values of the variable group velocity dispersion terms, which can be used to model various phenomena.
© 2019 Shanghai Jiaotong University. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license. (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Keywords: Coupled nonlinear Schrödinger equations; Davey–Stewartson system with variable coefficients; Sine-Gordon equation method; Solitary waves.