Characteristics of rogue waves on a soliton background in the general three-component nonlinear Schrödinger equation

Abstract Under investigation in this work is the general three-component nonlinear Schrodinger equation, which is an important integrable system. The new localized wave solutions of the equation are derived using a Darboux-dressing transformation with an asymptotic expansion. These localized waves display rogue waves on a multisoliton background. Furthermore, the main characteristics of the new localized wave solutions are analyzed with some graphics. Our results indicate that more abundant and novel localized waves may exist in the multi-component coupled equations than in the uncoupled ones.