Homogenization in the problem of long water waves over a bottom site with fast oscillations

DOI10.1134/S0001434614030055zbMath1315.35165MaRDI QIDQ2341988

V. V. Grushin, S. Yu. Dobrokhotov

Publication date: 8 May 2015

Published in: Mathematical Notes (Search for Journal in Brave)

zbMATH Keywords

small parameterhomogenizationasymptotic methodsadiabatic approximationsurface wavesrapidly oscillating function

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with fluid mechanics (35Q35) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Homogenization applied to problems in fluid mechanics (76M50)

Related Items (3)

Homogenization method in the problem of long wave propagation from a localized source in a basin over an uneven bottom ⋮ Asymptotics of the Cauchy problem for the one-dimensional Schrödinger equation with rapidly oscillating initial data and small addition to the smooth potential ⋮ Asymptotic theory of linear water waves in a domain with nonuniform bottom with rapidly oscillating sections

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Generalized Foldy-Wouthuysen transformation and pseudodifferential operators
• Asymptotic solutions of the Cauchy problem with localized initial conditions for linearized two-dimensional Boussinesq-type equations with variable coefficients
• Asymptotic expansions and the Maslov canonical opeator in the linear theory of water waves. I: Main constructions and equations for surface gravity waves
• Asymptotic solutions of the linear shallow-water equations with localized initial data
• Operator separation of variables for adiabatic problems in quantum and wave mechanics
• Localized wave and vortical solutions to linear hyperbolic systems and their application to linear shallow water equations
• Behavior near the focal points of asymptotic solutions to the Cauchy problem for the linearized shallow water equations with initial localized perturbations
• Approximate formulas for eigenvalues of the Laplace operator on a torus arising in linear problems with oscillating coefficients
• Averaging of linear operators, adiabatic approximation, and pseudodifferential operators
• Peierls substitution and the Maslov operator method

This page was built for publication: Homogenization in the problem of long water waves over a bottom site with fast oscillations