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

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

2002-10-17

arxiv.org/abs/nlin/0210038v1

Nonlinear Sciences

Chaotic Dynamics

4 pages, 2 figures

Scientific paper

10.1063/1.1622394

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 Schr\"odinger 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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