Weakly singular shock profiles for a non-dispersive regularization of shallow-water equations
Abstract
We study a regularization of the classical Saint-Venant (shallow-water) equations, recently introduced by D. Clamond and D. Dutykh (Commun. Nonl. Sci. Numer. Simulat. 55 (2018) 237-247). This regularization is non-dispersive and formally conserves mass, momentum and energy. We show that for every classical shock wave, the system admits a corresponding non-oscillatory traveling wave solution which is continuous and piecewise smooth, having a weak singularity at a single point where energy is dissipated as it is for the classical shock. The system also admits cusped solitary waves of both elevation and depression.
Domains
Fluid mechanics [physics.class-ph] Fluid Dynamics [physics.flu-dyn] Analysis of PDEs [math.AP] Classical Analysis and ODEs [math.CA] Numerical Analysis [math.NA] Atmospheric and Oceanic Physics [physics.ao-ph] Computational Physics [physics.comp-ph] Pattern Formation and Solitons [nlin.PS] Exactly Solvable and Integrable Systems [nlin.SI]Origin | Files produced by the author(s) |
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