Hamiltonian higher-order nonlinear Schrödinger equations for broader-banded waves on deep water

DOI10.1016/j.euromechflu.2011.09.008zbMath1258.76035OpenAlexW2016874812MaRDI QIDQ1940612

Philippe Guyenne, Walter Craig, Catherine Sulem

Publication date: 7 March 2013

Published in: European Journal of Mechanics. B. Fluids (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.euromechflu.2011.09.008

zbMATH Keywords

nonlinear Schrödinger equationHamiltonian systemssymplectic integratorswater wavesmodulation theoryDirichletNeumann operator

Mathematics Subject Classification ID

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

Related Items

Global well-posedness and scattering for the Dysthe equation in \(L^2(\mathbb{R}^2)\) ⋮ Hamiltonian form of an Extended Nonlinear Schrödinger Equation for Modelling the Wave field in a System with Quadratic and Cubic Nonlinearities ⋮ Deep learning neural networks for the third-order nonlinear Schrödinger equation: bright solitons, breathers, and rogue waves ⋮ Reduced-order prediction of rogue waves in two-dimensional deep-water waves ⋮ The water wave problem and Hamiltonian transformation theory ⋮ Computations of fully nonlinear hydroelastic solitary waves on deep water ⋮ Envelope Equations for Three-Dimensional Gravity and Flexural-Gravity Waves Based on a Hamiltonian Approach ⋮ An operator expansion method for computing nonlinear surface waves on a ferrofluid jet ⋮ A high-order nonlinear Schrödinger equation as a variational problem for the averaged Lagrangian of the nonlinear Klein-Gordon equation ⋮ Normal form transformations and Dysthe's equation for the nonlinear modulation of deep-water gravity waves ⋮ A Hamiltonian structure of the Isobe-Kakinuma model for water waves

Cites Work

• Unnamed Item
• Fourth order evolution equations and stability analysis for Stokes waves on arbitrary water depth
• A Hamiltonian approach to nonlinear modulation of surface water waves
• Numerical simulation of gravity waves
• Numerical simulation of three-dimensional nonlinear water waves
• Stability of bichromatic gravity waves on deep water
• A modified nonlinear Schrödinger equation for broader bandwidth gravity waves on deep water
• Hamiltonian long-wave approximations to the water-wave problem
• Hamiltonian form of the modified nonlinear Schrödinger equation for gravity waves on arbitrary depth
• Simulating Hamiltonian Dynamics
• On the dynamics of unsteady gravity waves of finite amplitude Part 1. The elementary interactions
• Long wave expansions for water waves over random topography
• Water waves over a random bottom
• On weakly nonlinear modulation of waves on deep water
• A High-Order Spectral Method for Nonlinear Water Waves over Moving Bottom Topography
• Note on a modification to the nonlinear Schrödinger equation for application to deep water waves
• Instabilities of finite-amplitude water waves
• The instabilities of gravity waves of finite amplitude in deep water II. Subharmonics
• Nonlinear modulation of gravity waves: a rigorous approach
• On reduced equations in the Hamiltonian theory of weakly nonlinear surface waves
• A PseudoSpectral Procedure for the Solution of Nonlinear Wave Equations with Examples from Free-Surface Flows
• Hamiltonian long–wave expansions for water waves over a rough bottom
• Hamiltonian long‐wave expansions for free surfaces and interfaces
• Solitary water wave interactions