Reflections from solitary waves in channels of decreasing depth

DOI10.1017/S0022112085001112zbMath0584.76024MaRDI QIDQ3707618

Alan C. Newell, C. J. Knickerbocker

Publication date: 1985

Published in: Journal of Fluid Mechanics (Search for Journal in Brave)

zbMATH Keywords

reflected waveperturbed Korteweg-de Vries equationapproximation for the right-going profilemass-flux conservation lawsregion of slowly changing depthright-going solitary wave

Mathematics Subject Classification ID

Solitary waves for incompressible inviscid fluids (76B25) Partial differential equations of mathematical physics and other areas of application (35Q99)

Related Items

Applications of KdV ⋮ Obliquely incident surface waves in shallow water of slowly varying depth ⋮ Hamiltonian models for the propagation of irrotational surface gravity waves over a variable bottom ⋮ Solitons, solitary waves, and voidage disturbances in gas-fluidized beds ⋮ A Korteweg-de Vries description of dark solitons in polariton superfluids ⋮ Weakly nonlinear waves in water of variable depth: variable-coefficient Korteweg-de Vries equation ⋮ The Classical Problem of Water Waves: a Reservoir of Integrable and Nearly-Integrable Equations ⋮ Auto-Bäcklund transformation, Lax pairs, and Painlevé property of a variable coefficient Korteweg–de Vries equation. I ⋮ Asymptotic Methods for Weakly Nonlinear and Other Water Waves ⋮ A note on the wave propagation in water of variable depth ⋮ An auto-Bäcklund transformation and exact solutions to a generalized KdV equation with variable coefficients and their applications ⋮ Propagation of axi-symmetric nonlinear shallow water waves over slowly varying depth ⋮ Propagation of solitary waves in channels of decreasing depth ⋮ Coastal Kelvin waves in the presence of a slowly varying topography ⋮ A note on an asymptotic solution of the cylindrical Korteweg-de Vries equation. ⋮ Shear fronts in slowly varying media

Cites Work

• Shelves and the Korteweg-de Vries equation
• On the Korteweg—de Vries equation for a gradually varying channel
• On an asymptotic solution of the Korteweg–de Vries equation with slowly varying coefficients
• The solitary wave in water of variable depth
• The solitary wave in water of variable depth. Part 2
• Amplification and decay of long nonlinear waves

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