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Wave Breaking and the Generation of Undular Bores in an Integrable Shallow Water System
Author(s) -
El G. A.,
Grimshaw R. H. J.,
Kamchatnov A. M.
Publication year - 2005
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/j.0022-2526.2005.01560.x
Subject(s) - hodograph , integrable system , euler's formula , mathematics , waves and shallow water , mechanics , mathematical analysis , classical mechanics , physics , thermodynamics
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.