Characteristics of the breather and rogue waves in a (2+1)-dimensional nonlinear Schrödinger equation

Abstract

© 2018 American Mathematical Society. Under investigation in this paper is a (2+1)-dimensional nonlinear Schrödinger equation (NLS), which is a generalisation of the NLS equation. By virtue of Wronskian determinants, an effective method is presented to succinctly construct the breather wave and rogue wave solutions of the equation. Furthermore, the main characteristics of the breather and rogue waves are graphically discussed. The results show that rogue waves can come from the extreme behavior of the breather waves. It is hoped that our results could be useful for enriching and explaining some related nonlinear phenomena.