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|Title: ||Wave breaking and the generation of undular bores in an integrable shallow-water system|
|Authors: ||El, G.A.|
Grimshaw, Roger H.J.
|Issue Date: ||2004|
|Abstract: ||The generation of an undular bore in the vicinity of a wave-breaking point is con-
sidered 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.|
|Description: ||This pre-print has been submitted, and accepted, to the journal, Studies in Applied Mathematics . The definitive version: EL, G.A., GRIMSHAW, R.H.J. and KAMCHATNOV, A.M., 2005. Wave breaking and the generation of undular bores in an integrable shallow-water system. Studies in Applied Mathematics, 114 (4), pp.395-411 is available at www.blackwell-synergy.com.|
|Appears in Collections:||Pre-prints (Maths)|
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