Wave breaking and the generation of undular bores in an integrable shallow-water system
preprintposted on 2005-07-22, 09:26 authored by Gennady El, Roger Grimshaw, A.M. Kamchatnov
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.
- Mathematical Sciences
NotesThis 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.