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 (24)

• Nonlinear Schrödinger Equation: Generalized Darboux Transformation and Rogue Wave Solutions
• Deterministic Vector Freak Waves
• A generating mechanism for higher order rogue waves
• Vector Rogue Waves and Baseband Modulation Instability in the Defocusing Regime
• Rogue waves in the Davey-Stewartson equation
• Financial rogue waves
• Financial Rogue Waves Appearing in the Coupled Nonlinear Volatility and Option Pricing Model
• Rogue waves emerging from the resonant interaction of three waves
• Rogue-wave solutions of a three-component coupled nonlinear Schrodinger equation
• High-order Rogue Waves in Vector Nonlinear Schrödinger Equations
• Nonautonomous "rogons" in the inhomogeneous nonlinear Schrodinger equation with variable coefficients
• The Rogue Wave and breather solution of the Gerdjikov-Ivanov equation
• Generalized perturbation (n, M)-fold Darboux transformations and multi-rogue-wave structures for the modified self-steepening nonlinear Schrodinger equation
• Localized nonlinear waves in a two-mode nonlinear fiber
• High-order rogue waves for the Hirota equation
• Extreme Superposition: Rogue Waves of Infinite Order and the Painlevé-III Hierarchy
• Darboux transformation and classification of solution for mixed coupled nonlinear Schrödinger equations
• Higher-order vector discrete rogue-wave states in the coupled Ablowitz-Ladik equations: exact solutions and stability
• High-order Rogue Wave solutions for the Coupled Nonlinear Schrödinger Equations-II
• Rogue waves, rational solitons, and modulational instability in an integrable fifth-order nonlinear Schroedinger equation
• N-wave interactions related to simple Lie algebras. Z_2- reductions and soliton solutions
• On N-wave type systems and their gauge equivalent
• 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)

• Non-degenerate multi-rogue waves and easy ways of their excitation
• Kadomtsev-Petviashvili equation: one-constraint method and lump pattern
• Measuring the rogue wave pattern triggered from Gaussian perturbations by deep learning