Soliton solutions of Davey–Stewartson equation by trial equation method and ansatz approach

Abstract

In this paper, we establish exact soliton solutions for the Davey–Stewartson equation. The trial equation method and the ansatz approach are used to construct exact 1-soliton solutions of this equation. We apply the trial equation method to establish solitary waves soliton, dark soliton and singular solitary waves soliton solutions. The Davey–Stewartson equation is the well-known example of integrable equations in two space dimensions, which arise as higher-dimensional generalizations of the nonlinear Schrodinger equation.