On transforms reducing one-dimensional systems of shallow-water to the wave equation with sound speed \(c^2=x\)

DOI10.1134/S0001434613050064zbMath1307.76010OpenAlexW1965681330MaRDI QIDQ358163

S. B. Medvedev, D. S. Minenkov, S. Yu. Dobrokhotov

Publication date: 16 August 2013

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

Full work available at URL: https://doi.org/10.1134/s0001434613050064

zbMATH Keywords

Jacobianhodograph transformationCarrier-Greenspan parametrizationpoint transformation

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Hydro- and aero-acoustics (76Q05)

Related Items (7)

Asymptotic solutions of the Cauchy problem for the nonlinear shallow water equations in a basin with a gently sloping beach ⋮ Asymptotics of long nonlinear propagating waves in a one-dimensional basin with gentle shores ⋮ Solution blowup for systems of shallow-water equations ⋮ Exact solutions of one-dimensional nonlinear shallow water equations over even and sloping bottoms ⋮ The generalized Carrier-Greenspan transform for the shallow water system with arbitrary initial and boundary conditions ⋮ Inheritance of generic singularities of solutions of a linear wave equation by solutions of isoentropic gas motion equations ⋮ Reflectionless wave propagation on shallow water with variable bathymetry and current

Cites Work

• Asymptotic solution of the one-dimensional wave equation with localized initial data and with degenerating velocity. I
• A class of exact algebraic localized solutions of the multidimensional wave equation
• Geometric asymptotics for a degenerate hyperbolic equation
• Rogue waves in nonlinear hyperbolic systems (shallow-water framework)
• Water waves of finite amplitude on a sloping beach
• Localized solutions of one-dimensional non-linear shallow-water equations with velocity $ c=\sqrt x$
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