A Model for the Periodic Water Wave Problem and Its Long Wave Amplitude Equations
From MaRDI portal
Publication:3294755
DOI10.1007/978-3-030-33536-6_8zbMath1442.35322OpenAlexW2990468878MaRDI QIDQ3294755
Roman Bauer, Guido Schneider, Patrick Cummings
Publication date: 29 June 2020
Published in: Nonlinear Water Waves (Search for Journal in Brave)
Full work available at URL: https://publikationen.bibliothek.kit.edu/1000088288/20053758
PDEs in connection with fluid mechanics (35Q35) KdV equations (Korteweg-de Vries equations) (35Q53) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) NLS equations (nonlinear Schrödinger equations) (35Q55)
Related Items
Cites Work
- Justification of the nonlinear Schrödinger equation for the evolution of gravity driven 2D surface water waves in a canal of finite depth
- 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
- Rigorous description of macroscopic wave packets in infinite periodic chains of coupled oscillators by modulation equations
- Justification of the nonlinear Schrödinger equation in spatially periodic media
- On the Korteweg-de Vries approximation for uneven bottoms
- A mathematical justification for Korteweg-de Vries equation and Boussinesq equation of water surface waves
- Justification of modulation equations for hyperbolic systems via normal forms
- The rigorous approximation of long-wavelength capillary-gravity waves
- A justification of the modulation approximation to the 3D full water wave problem
- The validity of the KdV approximation in case of resonances arising from periodic media
- 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
- Validity of the Korteweg-de Vries approximation for the two-dimensional water wave problem in the arc length formulation
- FROM THE KLEIN–GORDON–ZAKHAROV SYSTEM TO THE NONLINEAR SCHRÖDINGER EQUATION
- Justification of the nonlinear Schroedinger equation for a resonant Boussinesq model
- A Long Wave Approximation for Capillary-Gravity Waves and an Effect of the Bottom
- ASYMPTOTIC DECAY OF A ONE-DIMENSIONAL WAVE PACKET IN A NONLINEAR DISPERSIVE MEDIUM
- Influence of bottom topography on long water waves
- An existence theory for water waves and the boussinesq and korteweg-devries scaling limits
- The validity of modulation equations for extended systems with cubic nonlinearities
- Growth and Decay of Acceleration Waves in Incompressible Saturated Poroelastic Solids
- Nonlinear PDEs
- Bloch Theory and Spectral Gaps for Linearized Water Waves
- Approximation of Polyatomic FPU Lattices by KdV Equations
- The Korteweg–de Vries, Burgers and Whitham limits for a spatially periodic Boussinesq model