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

G. A. El, R. H.J. Grimshaw*, A. M. Kamchatnov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)
3 Downloads (Pure)

Abstract

The generation of an undular bore in the vicinity of a wave-breaking point is considered for the integrable Kaup-Boussinesq (KB) 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.

Original languageEnglish
Pages (from-to)395-411
Number of pages17
JournalStudies in Applied Mathematics
Volume114
Issue number4
Early online date31 Mar 2005
DOIs
Publication statusPublished - 1 May 2005
Externally publishedYes

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