Two-dimensional solitary wave solution to the quadratic-cubic nonlinear Schrödinger equation

Abstract

Abstract The Madelung fluid transformation is applied to find the link between the modified Korteweg-de Vries and the quadratic-cubic nonlinear Schrödinger equation. The two-dimensional solitary wave solution of the quadratic-cubic nonlinear Schrödinger equation will be determined by the Petviashvili method. This solution will be used for the initial condition for the time evolution to study the stability analysis. The spectral method is applied for the time evolution.