Dynamics of rogue waves on a multi-soliton background in a vector nonlinear Schrodinger equation

TL;DR

This paper derives higher order rogue wave solutions for a vector nonlinear Schrödinger equation, revealing complex structures on multisoliton backgrounds and advancing understanding of rogue wave phenomena in various physical systems.

Contribution

It introduces a method to construct semi-rational rogue wave solutions with multiple free parameters for the vector nonlinear Schrödinger equation, showing richer structures than in single-component systems.

Findings

Rogue waves on multisoliton backgrounds are explicitly constructed.

The solutions exhibit complex, richer structures compared to one-component systems.

Potential applications in optics, fluid dynamics, and other fields are discussed.

Abstract

General higher order rogue waves of a vector nonlinear Schrodinger equation (Manakov system) are derived using a Darboux-dressing transformation with an asymptotic expansion method. The Nth order semi-rational 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. The study of 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 and so on.