Asymptotic solutions of the Cauchy problem for the nonlinear shallow water equations in a basin with a gently sloping beach

DOI10.1134/S1061920822010034zbMath1490.76035MaRDI QIDQ2120146

S. Yu. Dobrokhotov, D. S. Minenkov, Vladimir E. Nazaikinskii

Publication date: 31 March 2022

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

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) Asymptotic methods, singular perturbations applied to problems in fluid mechanics (76M45) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)

Related Items (4)

Asymptotics of long nonlinear coastal waves in basins with gentle shores ⋮ Nonlinear long standing waves with support bounded by caustics or localized in the vicinity of a two-link trajectory ⋮ Asymptotics of long nonlinear propagating waves in a one-dimensional basin with gentle shores ⋮ Nonlinear effects and run-up of coastal waves generated by billiards with semi-rigid walls in the framework of shallow water theory

Cites Work

• Unnamed Item
• On transforms reducing one-dimensional systems of shallow-water to the wave equation with sound speed \(c^2=x\)
• On a homogenization method for differential operators with oscillating coefficients
• Homogenization method in the problem of long wave propagation from a localized source in a basin over an uneven bottom
• Simple asymptotics for a generalized wave equation with degenerating velocity and their applications in the linear long wave run-up problem
• Asymptotics of the solutions of the one-dimensional nonlinear system of equations of shallow water with degenerate velocity
• Uniformization of equations with Bessel-type boundary degeneration and semiclassical asymptotics
• Method for the analysis of long water waves taking into account reflection from a gently sloping beach
• 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$
• Homogenization of the Cauchy Problem for the Wave Equation with Rapidly Varying Coefficients and Initial Conditions

This page was built for publication: Asymptotic solutions of the Cauchy problem for the nonlinear shallow water equations in a basin with a gently sloping beach