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

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

doi:10.1111/j.0022-2526.2005.01560.x

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 journal › Article › peer-review

33 Citations (Scopus)

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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 (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 language	English
Pages (from-to)	395-411
Number of pages	17
Journal	Studies in Applied Mathematics
Volume	114
Issue number	4
Early online date	31 Mar 2005
DOIs	https://doi.org/10.1111/j.0022-2526.2005.01560.x
Publication status	Published - 1 May 2005
Externally published	Yes

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Wave breaking and the generation of undular bores in an integrable shallow water systemAccepted author manuscript, 140 KBLicence: CC BY-NC-ND

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Y1 - 2005/5/1

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AB - 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.

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

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