Dynamics of Rogue Waves on a Multisoliton Background in a Vector Nonlinear Schrödinger Equation

Abstract

General higher-order rogue waves of a vector nonlinear Schrödinger equation (Manakov system) are derived using a Darboux-dressing transformation with an asymptotic expansion method. The $N$th-order semirational solutions containing 3N free parameters are expressed in separation-of-variables form. These solutions exhibit rogue waves on a multisoliton background. They demonstrate that the structure of rogue waves in this two-component system is richer than that in a one-component system. Our results would be of much importance in understanding and predicting rogue wave phenomena arising in nonlinear and complex systems, including optics, fluid dynamics, Bose--Einstein condensates, and finance.