Abstract
•The sine-Gordon equation method is modified so as to be applicable to systems with variable coefficients containing imaginary parts.•The new modified method is applied on both coupled Schrödinger equations and Davey–Stewartson system with variable coefficients for there importance in ocean engineering and optics.•Novel solitary wave solutions are obtained for both coupled nonlinear Schrödinger equations and Davey–Stewartson system with variable coefficients.•Some figures for the solitary wave solutions of the coupled nonlinear Schrödinger equations are given to illustrate the propagation behavior of the solitary wave.•The new modified sine-Gordon equation method can be used for solving other systems of partial dintial equations arising in ocean engineering and optics.
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.