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

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.