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Instability of two interacting, quasi-monochromatic waves in shallow water

M. Onorato·D. Ambrosi·A. R. Osborne·M. Serio
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Abstract

We study the nonlinear interactions of waves with a doubled-peaked power spectrum in shallow water. The starting point is the prototypical equation for nonlinear uni-directional waves in shallow water, i.e. the Korteweg de Vries equation. Using a multiple-scale technique two defocusing coupled Nonlinear Schrödinger equations are derived. We show analytically that plane wave solutions of such a system can be unstable to small perturbations. This surprising result suggests the existence of a new energy exchange mechanism which could influence the behaviour of ocean waves in shallow water.

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M. Onorato, D. Ambrosi, A. R. Osborne, M. Serio. 2002-10-17. Instability of two interacting, quasi-monochromatic waves in shallow water. https://doi.org/10.1063/1.1622394

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