Long-time dynamics of the modulational instability of deep water waves

DOI10.1016/S0167-2789(01)00183-XzbMath1049.76005OpenAlexW2163618760MaRDI QIDQ5940222

Constance M. Schober, Mark J. Ablowitz, J. Hammack, Diane M. Henderson

Publication date: 2001

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0167-2789(01)00183-x

zbMATH Keywords

nonlinear Schrödinger equationStokes wavesFloquet spectral decomposition

Mathematics Subject Classification ID

Experimental work for problems pertaining to fluid mechanics (76-05) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Interfacial stability and instability in hydrodynamic stability (76E17)

Related Items (16)

Melnikov analysis and inverse spectral analysis of rogue waves in deep water ⋮ Freak waves as nonlinear stage of Stokes wave modulation instability ⋮ 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. ⋮ Chaotic-like behavior of modulated waves in a nonlinear discrete LC transmission line. ⋮ A Hamiltonian approach to nonlinear modulation of surface water waves ⋮ The modulational instability of Stokes waves on the surface of finite-depth fluid ⋮ Dispersion managed generation of Peregrine solitons and Kuznetsov-Ma breather in an optical fiber ⋮ Predicting rogue waves in random oceanic sea states ⋮ On the ill-posedness for a nonlinear Schrödinger-Airy equation ⋮ Persistence of solutions to higher order nonlinear Schrödinger equation ⋮ Rogue waves, dissipation, and downshifting ⋮ The finite-gap method and the periodic NLS Cauchy problem of anomalous waves for a finite number of unstable modes ⋮ Modulational instability in a purely nonlinear coupled complex Ginzburg–Landau equations through a nonlinear discrete transmission line ⋮ The linear and nonlinear instability of the Akhmediev breather ⋮ Homoclinic chaos increases the likelihood of rogue wave formation

Cites Work

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• On the numerical solution of the sine-Gordon equation. II: Performance of numerical schemes
• Nonlinear normal modes for the Toda chain
• Geometry of the modulational instability. III: Homoclinic orbits for the periodic sine-Gordon equation
• Chaotic and homoclinic behavior for numerical discretizations of the nonlinear Schrödinger equation
• A modified nonlinear Schrödinger equation for broader bandwidth gravity waves on deep water
• Chaotic transport and integrable instabilities in a near-integrable, many-particle, Hamiltonian lattice
• Effects of symmetry on instability-driven chaotic energy transport in near-integrable, Hamiltonian systems
• A quasi-periodic route to chaos in a near-integrable PDE
• Mel'nikov analysis of numerically induced chaos in the nonlinear Schrödinger equation
• On the numerical solution of the sine-Gordon equation. I: Integrable discretizations and homoclinic manifolds
• Note on a modification to the nonlinear Schrödinger equation for application to deep water waves
• Nonlinear deep water waves: Theory and experiment
• The disintegration of wave trains on deep water Part 1. Theory
• Wave Instabilities
• Mel'nikov analysis of a symmetry-breaking perturbation of the NLS equation

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