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Modulational instabilities and Fermi-Pasta-Ulam recurrence in a coupled long wave-short wave system, with a mismatch in group velocity
preprint
posted on 2006-01-27, 11:31 authored by C.K. Poon, Roger Grimshaw, K.W. ChowThe resonance of two envelopes of short (capillary) waves with a common long (gravity)
wave component is considered. A mismatch in group velocity is incorporated and the
resonance conditions need not be satisfied exactly. This slight detuning permits a wider
choice of modes and consequently, a much richer set of dynamics. The linear instability of
plane waves is studied, and the dominant unstable wave numbers are identified. The
subsequent fully nonlinear evolution of these perturbed plane waves is investigated by direct
numerical simulations. The Fermi – Pasta – Ulam recurrence phenomenon is observed.
History
School
- Science
Department
- Mathematical Sciences
Pages
367295 bytesPublication date
2006Notes
This is a pre-print.Language
- en