Asymptotics of shallow water equations on the sphere

DOI10.1134/S1061920814040025zbMath1311.76012OpenAlexW2054514837MaRDI QIDQ2344176

S. Yu. Dobrokhotov, Anton A. Tolchennikov, Brunello Tirozzi

Publication date: 12 May 2015

Published in: Russian Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1061920814040025

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15)

Related Items (4)

Asymptotics of linear water waves generated by a localized source near the focal points on the leading edge ⋮ Simple asymptotics for a generalized wave equation with degenerating velocity and their applications in the linear long wave run-up problem ⋮ Method for the analysis of long water waves taking into account reflection from a gently sloping beach ⋮ Behavior of the solution of the Klein-Gordon equation with a localized initial condition

Cites Work

• New formulas for Maslov's canonical operator in a neighborhood of focal points and caustics in two-dimensional semiclassical asymptotics
• Full nonlinear dispersion model of shallow water equations on a rotating sphere
• 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
• Simple asymptotic solution of the Cauchy-Poisson problem for head waves
• Analysis of the Turkel-Zwas scheme for the two-dimensional shallow water equations in spherical coordinates
• Description of tsunami propagation based on the Maslov canonical operator
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