Resonant Davey-Stewartson system: Dark, bright mixed dark-bright optical and other soliton solutions

Abstract

We aim to determine the analytical solutions for the Davey-Stewartson (RDS) equations in (2+1)-dimensions using the extended sine-Gordon equation expansion method. It is a natural two-dimensional form of the nonlinear Schrodinger equation. As a first step, we change the imaginary (2+1)-dimensional RDS model to a system of nonlinear ordinary differential equations, then we apply the sine-Gordon method. With the use of Wolfram Mathematica software, we try to find novel solutions to the resulting system of the nonlinear differential equation. Constructed solutions are drawn in 2D and 3D-dimensions graphs to more realize their characteristics.