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

G. A. El; R. H. J. Grimshaw; A. M. Kamchatnov

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

G. A. El·R. H. J. Grimshaw·A. M. Kamchatnov

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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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G. A. El, R. H. J. Grimshaw, A. M. Kamchatnov. 2004-12-22. Wave breaking and the generation of undular bores in an integrable shallow-water system. https://arxiv.org/abs/nlin/0412060

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