Rogue waves in the (2+1)-dimensional nonlinear Schrodinger equations

Abstract

Purpose – The purpose of this paper is to construct analytical solutions of the (2+1)-dimensional nonlinear Schrodinger equations, and the existence of rogue waves and their localized structures are studied. Design/methodology/approach – Function transformation and variable separation method are applied to the (2+1)-dimensional nonlinear Schrodinger equations. Findings – A series of analytical solutions including rogue wave solutions for the (2+1)-dimensional nonlinear Schrodinger equations are constructed. Localized structures of rogue waves confirm the presence of large amplitude wave wall. Research limitations/implications – The localized structures of rogue waves are displayed by analytical solutions and figures. The authors just find some of them and others still to be found. Originality/value – These results may help to investigate the localized structures and the behavior of rogue waves for nonlinear evolution equations. Applying two different function transformations and variable separation functions to two different states of the equations, respectively, to construct the solutions of the (2+1)-dimensional nonlinear Schrodinger equations. Rogue wave solutions are enumerated and their figures are partly displayed.