Justification of the nonlinear Schroedinger equation for a resonant Boussinesq model

DOI10.1512/iumj.2006.55.2824zbMath1194.35362OpenAlexW1996271057MaRDI QIDQ3422448

Publication date: 13 February 2007

Published in: Indiana University Mathematics Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1512/iumj.2006.55.2824

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03) Existence, uniqueness, and regularity theory for incompressible inviscid fluids (76B03)

Related Items

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 ⋮ Global well-posedness of 2D non-focusing Schrödinger equations via rigorous modulation approximation ⋮ Justification of the 2D NLS equation for a fourth order nonlinear wave equation - quadratic resonances do not matter much in case of analytic initial conditions ⋮ The Validity of Whitham's Approximation for a Klein--Gordon--Boussinesq Model ⋮ On the mathematical description of time-dependent surface water waves ⋮ Justification of the nonlinear Schrödinger approximation for a quasilinear Klein-Gordon equation ⋮ Existence of long time solutions and validity of the nonlinear Schrödinger approximation for a quasilinear dispersive equation ⋮ NLS approximation of the Euler-Poisson system for a cold ion-acoustic plasma ⋮ Validity of the nonlinear Schrödinger approximation for quasilinear dispersive systems with more than one derivative ⋮ Validity of the nonlinear Schrödinger approximation for the two-dimensional water wave problem with and without surface tension in the arc length formulation ⋮ A Model for the Periodic Water Wave Problem and Its Long Wave Amplitude Equations ⋮ Justification of the NLS approximation for the KdV equation using the Miura transformation ⋮ Bounds for the nonlinear Schrödinger approximation of the Fermi–Pasta–Ulam system ⋮ Multifrequency NLS Scaling for a Model Equation of Gravity-Capillary Waves ⋮ Numerical evidence for the validity of the NLS approximation in systems with a quasilinear quadratic nonlinearity

This page was built for publication: Justification of the nonlinear Schroedinger equation for a resonant Boussinesq model