Wave breaking and the generation of undular bores in an integrable shallow-water system

2004/12/22 by G. A. El, R. H. J. Grimshaw, A. M. Kamchatnov · 1 citation
Physics and Astronomy · #nlin.PS #nlin.SI

paper · pdf

published as Stud. Appl. Math. 114 (4) 395-411 (2005) · 14 pages, 4 figures

arxiv created 2004/12/22 · arxiv updated 2009/12/01

Abstract

The generation of an undular bore in the vicinity of a wave-breaking point is considered for the integrable Kaup-Boussinesq shallow water system. In the framework of the Whitham modulation theory, an analytic solution of the Gurevich-Pitaevskii type of problem for a generic "cubic" breaking regime is obtained using a generalized hodograph transform, and a further reduction to a linear Euler-Poisson equation. The motion of the undular bore edges is investigated in detail.

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