A generating mechanism for higher order rogue waves

Abstract

We introduce a mechanism for generating higher order rogue waves (HRWs) of the nonlinear Schrödinger(NLS) equation: the progressive fusion and fission of $n$ degenerate breathers associated with a critical eigenvalue ${\lambda }_0$, creates an order $n$ HRW. By adjusting the relative phase of the breathers at the interacting area, it is possible to obtain different types of HRWs. The value ${\lambda }_0$ is a zero point of the eigenfunction of the Lax pair of the NLS equation and it corresponds to the limit of the period of the breather tending to infinity. By employing this mechanism we prove two conjectures regarding the total number of peaks, as well as a decomposition rule in the circular pattern of an order $n$ HRW.

12 pages, 13 figures, To appear in Phys.Rev.E

References in corpus (5)

• Deterministic Vector Freak Waves
• Observation of an Inverse Energy Cascade in Developed Acoustic Turbulence in Superfluid Helium
• Rogue waves in the Davey-Stewartson equation
• Capillary rogue waves
• Harnessing and control of optical rogue waves in supercontinuum generation

Cited by in corpus (63)

• Breather and Rogue Wave solutions of a Generalized Nonlinear Schrodinger Equation
• High-order Rogue Waves in Vector Nonlinear Schrödinger Equations
• Few-cycle optical rogue waves:complex modified Korteweg-de Vries equation
• Rogue waves of the Hirota and the Maxwell-Bloch equations
• Quantitative Relation between Modulational Instability and Several Well-known Nonlinear Excitations
• State Transition Induced by Higher-order Effects and Background Frequency
• The higher order Rogue Wave solutions of the Gerdjikov-Ivanov equation
• Generation of higher-order rogue waves from multi-breathers by double degeneracy in an optical fibre
• High-order rogue waves for the Hirota equation
• Darboux transformation and classification of solution for mixed coupled nonlinear Schrödinger equations
• Rational W-shaped Optical Soliton on Continuous Wave in Presence of Kerr Dispersion and Stimulated Raman Scattering
• High-order Rogue Wave solutions for the Coupled Nonlinear Schrödinger Equations-II
• Semi-rational solutions of the third-type Davey-Stewartson equation
• Rogue Waves In Nonlinear Schrödinger Models with Variable Coefficients: Application to Bose-Einstein Condensates
• Trajectory Characters of Rogue Waves
• Periodic and rational solutions of the reduced Maxwell-Bloch equations
• Manipulating matter-rogue waves and breathers in Bose-Einstein condensates
• Universal rogue wave patterns associated with the Yablonskii-Vorob'ev polynomial hierarchy
• General high-order rogue waves of the (1+1)-dimensional Yajima-Oikawa system
• Theoretical and experimental evidence of non-symmetric doubly localized rogue waves
• Stable Soliton Excitations in Modulational Instability Regime with the Fourth-order Effects
• Two (2 + 1)-dimensional integrable nonlocal nonlinear Schrodinger equations: Breather, rational and semi-rational solutions
• Higher-order vector Peregrine solitons and asymptotic estimates for the multi-component nonlinear Schrödinger equations
• Darboux transformation of nonisospectral coupled Gross-Pitaevskii equation and its multi-component generalization
• Generalized Darboux transformation and N-th order rogue wave solution of a general coupled nonlinear Schrödinger equations
• Early Detection of Rogue Waves by the Wavelet Transforms
• High-order rogue waves of a long wave-short wave model
• Modulation instability, rogue waves and spectral analysis for the sixth-order nonlinear Schrodinger equation
• Non-degenerate multi-rogue waves and easy ways of their excitation
• Rogue wave triggered at a critical frequency of a nonlinear resonant medium
• Multivalley dark solitons in multicomponent Bose-Einstein condensates with repulsive interactions
• The height of an $n$th-order fundamental rogue wave for the nonlinear Schrödinger equation
• Generating mechanism and dynamic of the smooth positons for the derivative nonlinear Schrödinger equation
• Localized excitations and interactional solutions for the reduced Maxwell-Bloch equations
• Two-dimensional rogue waves on zero background of the Davey-Stewartson II equation
• Optical rogue waves and W-shaped solitons in the multiple self-induced transparency system
• Multiple rogue wave solutions for (2+1)-dimensional Boussinesq equation
• Families of exact solutions of a new extended (2+1)-dimensional Boussinesq equation
• Chess-Board-Like Spatio-Temporal Interference Patterns and Their Excitation
• Dynamics of Rogue Wave Excitation Pattern on Stripe Phase Backgrounds in a Two-component Bose-Einstein Condensate
• On Rogue wave in the Kundu-DNLS equation
• Parity-time-symmetric vector rational rogue wave solutions in any n-component nonlinear Schrödinger models
• Numerical spectral synthesis of breather gas for the focusing nonlinear Schrödinger equation
• Construction of rational solutions of the real modified Korteweg-de Vries equation from its periodic solutions
• Rogue waves in a resonant erbium-doped fiber system with higher-order effects
• Amplification of matter rogue waves and breathers in quasi-two-dimensional Bose-Einstein condensates
• State transition induced by self-steepening and self phase-modulation
• Asymptotic dynamics of higher-order lumps in the Davey-Stewartson II equation
• Controllable generations of several nonlinear waves in optical fibers with third-order dispersion
• Darboux transformation of the second-type derivative nonlinear Schrödinger equation
• The solutions of classical and nonlocal nonlinear Schrödinger equations with nonzero backgrounds: Bilinearisation and reduction approach
• Vector rogue waves in spin-1 Bose-Einstein condensates with spin-orbit coupling
• Galilean-transformed solitons and supercontinuum generation in dispersive media
• Darboux transformation and positons of the inhomogeneous Hirota and the Maxwell-Bloch equation
• The hierarchy of higher order solutions of the derivative nonlinear Schrödinger equation
• Measuring the rogue wave pattern triggered from Gaussian perturbations by deep learning
• On a periodic solution of the focusing nonlinear Schrödinger equation
• Rogue wave patterns in the nonlinear Schrödinger equation
• The rational solutions of the mixed nonlinear Schrödinger equation
• Rogue Wave Morphology in Broadband Nonbreaking Seas
• N-order bright and dark rogue waves in a Resonant erbium-doped Fibre system
• The three-level coupled Maxwell-Bloch equations: rogue waves, semirational rogue waves and W-shaped solitons
• Correlated many-body quantum dynamics of the Peregrine soliton