Exact solutions of one-dimensional nonlinear shallow water equations over even and sloping bottoms

DOI10.1007/s11232-014-0143-4zbMath1297.76027OpenAlexW1990805769MaRDI QIDQ461602

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

Publication date: 13 October 2014

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11232-014-0143-4

zbMATH Keywords

symmetry groupinvariant solution

Mathematics Subject Classification ID

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

Related Items (6)

Conservative invariant finite‐difference schemes for the modified shallow water equations in Lagrangian coordinates ⋮ Asymptotics of long nonlinear propagating waves in a one-dimensional basin with gentle shores ⋮ Conformal invariance and new exact solutions of the elastostatics equations ⋮ Lie symmetries of two-dimensional shallow water equations with variable bottom topography ⋮ О решении одной обратной задачи для уравнений мелкой воды в бассейне с переменной глубиной ⋮ Reflectionless wave propagation on shallow water with variable bathymetry and current

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On transforms reducing one-dimensional systems of shallow-water to the wave equation with sound speed \(c^2=x\)
• 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
• Linear autonomy conditions for the basic Lie algebra of a system of linear differential equations
• Asymptotics of the solutions of the one-dimensional nonlinear system of equations of shallow water with degenerate velocity
• On the symmetry classification and conservation laws for quasilinear differential equations of second order
• 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$
• Symmetries of Differential Equations. The Hypergeometric and Euler–Darboux Equations

This page was built for publication: Exact solutions of one-dimensional nonlinear shallow water equations over even and sloping bottoms