Homoclinic chaos increases the likelihood of rogue wave formation

DOI10.1016/S0375-9601(02)00576-5zbMath0995.76010MaRDI QIDQ1602310

Constance M. Schober, Annalisa M. Calini

Publication date: 19 June 2002

Published in: Physics Letters. A (Search for Journal in Brave)

zbMATH Keywords

perturbationshyperbolic structuresdeep water wavesdispersive nonlinear Schrö dinger equation

Mathematics Subject Classification ID

Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items (25)

Breather interactions and higher-order nonautonomous rogue waves for the inhomogeneous nonlinear Schrödinger Maxwell-Bloch equations ⋮ Generation mechanism of rogue waves for the discrete nonlinear Schrödinger equation ⋮ Nonlinear damped spatially periodic breathers and the emergence of soliton-like rogue waves ⋮ Solution of a nonlinear Schrödinger equation in the form of two-phase freak waves ⋮ Characterizing JONSWAP rogue waves and their statistics via inverse spectral data ⋮ Long time interaction of envelope solitons and freak wave formations ⋮ Melnikov analysis and inverse spectral analysis of rogue waves in deep water ⋮ Nonlinear analysis and simulations of measured freak wave time series ⋮ The exact rogue wave recurrence in the NLS periodic setting via matched asymptotic expansions, for 1 and 2 unstable modes ⋮ Physical mechanisms of the rogue wave phenomenon. ⋮ Short‐Lived Large‐Amplitude Pulses in the Nonlinear Long‐Wave Model Described by the Modified Korteweg–De Vries Equation ⋮ Efficiency of exponential time differencing schemes for nonlinear Schrödinger equations ⋮ Numerical investigation of the stability of the rational solutions of the nonlinear Schrödinger equation ⋮ Predicting rogue waves in random oceanic sea states ⋮ Linear instability of the Peregrine breather: numerical and analytical investigations ⋮ Rogue waves, rational solitons and wave turbulence theory ⋮ Dynamics of the higher-order rogue waves for a generalized mixed nonlinear Schrödinger model ⋮ Rogue waves, dissipation, and downshifting ⋮ Nearly linear dynamics of nonlinear dispersive waves ⋮ Influence of wind on extreme wave events: experimental and numerical approaches ⋮ Peregrine solitons and algebraic soliton pairs in Kerr media considering space-time correction ⋮ Talbot carpets by rogue waves of extended nonlinear Schrödinger equations ⋮ The finite-gap method and the periodic NLS Cauchy problem of anomalous waves for a finite number of unstable modes ⋮ The linear and nonlinear instability of the Akhmediev breather ⋮ The effects of wind and nonlinear damping on rogue waves and permanent downshift

Cites Work

• Nonlinear wave focusing on water of finite depth
• Geometry of the modulational instability. III: Homoclinic orbits for the periodic sine-Gordon equation
• The nonlinear dynamics of rogue waves and holes in deep-water gravity wave trains
• A modified nonlinear Schrödinger equation for broader bandwidth gravity waves on deep water
• Mel'nikov analysis of numerically induced chaos in the nonlinear Schrödinger equation
• Note on a modification to the nonlinear Schrödinger equation for application to deep water waves
• Mel'nikov analysis of a symmetry-breaking perturbation of the NLS equation
• Long-time dynamics of the modulational instability of deep water waves
• Unsteady water wave modulations: Fully nonlinear solutions and comparison with the nonlinear Schrödinger equation.
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