General coupled nonlinear Schrödinger equation: Breather waves and rogue waves on a soliton background, and dynamics

Abstract

Under investigation in this work is the general coupled nonlinear Schrödinger (gCNLS) equation, which can be reduced to several integrable equations. By using Darboux-dressing transformation, the new localized wave solutions of the equation are constructed. These solutions exhibit breather waves and rogue waves on a multi-soliton background. Moreover, the dynamics of these solutions is analyzed with some graphics. Our results can be of much importance in enriching and predicting rogue wave phenomena arising in nonlinear wave fields.