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We study the nonlinear interactions of waves with a doubled-peaked powerspectrum in shallow water. The starting point is the prototypical equation fornonlinear uni-directional waves in shallow water, i.e. the Korteweg de Vriesequation. Using a multiple-scale technique two defocusing coupled NonlinearSchr\"odinger equations are derived. We show analytically that plane wavesolutions of such a system can be unstable to small perturbations. Thissurprising result suggests the existence of a new energy exchange mechanismwhich could influence the behaviour of ocean waves in shallow water.Comment: 4 pages, 2 figure

Interaction of two quasi-monochromatic waves in shallow water