Solitary wave solutions for the variable-coefficient coupled nonlinear Schrödinger equations and Davey–Stewartson system using modified sine-Gordon equation method

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.