Higher-order vector Peregrine solitons and asymptotic estimates for the multi-component nonlinear Schrödinger equations

Abstract

We first report the first- and higher-order vector Peregrine solitons (alias rational rogue waves) for the any multi-component NLS equations based on the loop group theory, an explicit (n + 1)-multiple eigenvalue of a characteristic polynomial of degree (n + 1) related to the condition of Benjamin-Feir instability, and inverse functions. Particularly, these vector rational rogue waves are parity-time symmetric for some parameter constraints. A systematic and effective approach is proposed to study the asymptotic behaviors of these vector rogue waves such that the decompositions of rogue waves are related to the so-called governing polynomials, which pave a powerful way in the study of vector rogue wave structures of the multi-component integrable systems. The vector rogue waves with maximal amplitudes can be determined via the parameter vectors, which is interesting and useful in the multi-component physical systems.

42 pages, 7 figures

References in corpus (6)

• Vector Rogue Waves and Baseband Modulation Instability in the Defocusing Regime
• Rogue-wave solutions of a three-component coupled nonlinear Schrodinger equation
• Localized nonlinear waves in a two-mode nonlinear fiber
• Higher-order vector discrete rogue-wave states in the coupled Ablowitz-Ladik equations: exact solutions and stability
• Parity-time-symmetric vector rational rogue wave solutions in any n-component nonlinear Schrödinger models
• Universal patterns of rogue waves

Cited by in corpus (3)

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