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arXiv · 1404.2988

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

Gui Mu·Zhenyun Qin·Roger Grimshaw
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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.

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Gui Mu, Zhenyun Qin, Roger Grimshaw. 2014-04-11. Dynamics of rogue waves on a multi-soliton background in a vector nonlinear Schrodinger equation. https://arxiv.org/abs/1404.2988

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