Modulation instability, rogue waves and spectral analysis for the sixth-order nonlinear Schrodinger equation
arXiv:1908.04941 · doi:10.1016/j.cnsns.2020.105284
Abstract
Modulation instability, rogue wave and spectral analysis are investigated for the nonlinear Schrodinger equation with the higher-order terms. The modulation instability distribution characteristics from the sixth-order to the eighth-order nonlinear Schrodinger equations are studied. Higher-order dispersion terms are closely related to the distribution of modulation stability regime, and n-order dispersion term corresponds to modulation stability curves in the modulation instability band. Based on the generalized Darboux transformation method, the higher-order rational solutions are constructed. Then the compact algebraic expression of the Nth-order rogue wave is given. Dynamic phenomena of first- to third-order rogue waves are illustrated, which exhibit meaningful structures. Two arbitrary parameters play important roles in the rogue wave solution. One can control deflection of crest of rogue wave and its width, while the other can cause the change of width and amplitude of rogue wave. When it comes to the third-order rogue wave, three typical nonlinear wave constructions, namely fundamental, circular and triangular are displayed and discussed. Through the spectral analysis on first-order rogue wave, when these parameters satisfy certain conditions, it occurs a transition between W-shaped soliton and rogue wave.
arXiv comment17 pages, 10 figures
References in corpus (15)
- Nonlinear Schrödinger Equation: Generalized Darboux Transformation and Rogue Wave Solutions
- General high-order rogue waves and their dynamics in the nonlinear Schroedinger equation
- A generating mechanism for higher order rogue waves
- Rogue waves in the atmosphere
- Breather transition dynamics, Peregrine combs/walls and modulation instability in a variable-coefficient nonlinear Schrödinger equation with higher-order effects
- Multi-soliton, multi-breather and higher-order rogue wave solutions to the complex short pulse equation
- Quantitative Relation between Modulational Instability and Several Well-known Nonlinear Excitations
- Rogue waves, rational solitons, and modulational instability in an integrable fifth-order nonlinear Schroedinger equation
- Symmetric and asymmetric optical multi-peak solitons on a continuous wave background in the femtosecond regime
- Periodic and rational solutions of the reduced Maxwell-Bloch equations
- Stable Soliton Excitations in Modulational Instability Regime with the Fourth-order Effects
- Rogue Wave Spectra of the Kundu-Eckhaus Equation
- Variational Approach to the Modulational Instability
- Localized excitations and interactional solutions for the reduced Maxwell-Bloch equations
- Optical rogue waves and W-shaped solitons in the multiple self-induced transparency system