Proof of modulational instabilityÌýof Stokes waves
Proof of modulational instabilityÌýof Stokes waves
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Huy Q. Nguyen, Brown University
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It is proven that small-amplitude steady periodic water waves with infinite depth are unstable with respect to long-wave perturbations.ÌýThis modulational instability was first observedÌýmore than half a century ago by Benjamin and Feir.ÌýIt has never been proven rigorously except in the case of finite depth. We provide a completely different and self-contained approach to prove the spectral modulational instability for water waves in both the finite and infinite depth cases. This is joint work with W. Strauss.