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arXiv · 2007.05018

Proof of modulational instability of Stokes waves in deep water

Huy Q. Nguyen·Walter A. Strauss
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Abstract

It is proven that small-amplitude steady periodic water waves with infinite depth are unstable with respect to long-wave perturbations. This modulational instability was first observed more than half a century ago by Benjamin and Feir. It has been proven rigorously only 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.

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Huy Q. Nguyen, Walter A. Strauss. 2020-07-09. Proof of modulational instability of Stokes waves in deep water. https://arxiv.org/abs/2007.05018

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