Justification of the nonlinear Schrödinger equation for the evolution of gravity driven 2D surface water waves in a canal of finite depth

DOI10.1007/s00205-015-0937-zzbMath1334.35313OpenAlexW2116104023MaRDI QIDQ266889

Guido Schneider, Wolf-Patrick Düll, C. Eugene Wayne

Publication date: 7 April 2016

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00205-015-0937-z

Mathematics Subject Classification ID

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

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Cites Work

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• The NLS approximation makes wrong predictions for the water wave problem in case of small surface tension and spatially periodic boundary conditions
• A rigorous justification of the modulation approximation to the 2D full water wave problem
• Global wellposedness of the 3-D full water wave problem
• Justification of the NLS approximation for a quasilinear water wave model
• Capillary-gravity waves for an incompressible ideal fluid
• The nonlinear dynamics of rogue waves and holes in deep-water gravity wave trains
• Almost global wellposedness of the 2-D full water wave problem
• Sur les ondes de surface de l'eau avec une justification mathématique des équations des ondes en eau peu profonde
• Gravity waves on the free surface of an incompressible perfect fluid of finite depth
• Approximation of the Korteweg-de Vries equation by the nonlinear Schrödinger equation
• Well-posedness in Sobolev spaces of the full water wave problem in 2D
• The modulational regime of three-dimensional water waves and the Davey-Stewartson system
• Justification of modulation equations for hyperbolic systems via normal forms
• The rigorous approximation of long-wavelength capillary-gravity waves
• Global solutions for the gravity water waves system in 2d
• A justification of the modulation approximation to the 3D full water wave problem
• Justification and failure of the nonlinear Schrödinger equation in case of non-trivial quadratic resonances
• The long-wave limit for the water wave problem I. The case of zero surface tension
• KP description of unidirectional long waves. The model case
• Justification of the nonlinear Schroedinger equation for a resonant Boussinesq model
• ASYMPTOTIC DECAY OF A ONE-DIMENSIONAL WAVE PACKET IN A NONLINEAR DISPERSIVE MEDIUM
• The zero surface tension limit of three-dimensional water waves
• An existence theory for water waves and the boussinesq and korteweg-devries scaling limits
• Nonlinear modulation of gravity waves: a rigorous approach
• The validity of modulation equations for extended systems with cubic nonlinearities
• Well-posedness in Sobolev spaces of the full water wave problem in 3-D
• Well-Posedness of Vortex Sheets with Surface Tension
• Well-posedness of the water-waves equations
• Estimates for the three-wave interaction of surface water waves
• Validity and Limitation of the Newell‐Whitehead Equation
• Global Existence for Capillary Water Waves
• The zero surface tension limit two‐dimensional water waves
• Global solutions for the gravity water waves equation in dimension 3