Proof of modulational instability of Stokes waves in deep water
Analysis of PDEs
2021-07-05 v2 Fluid Dynamics
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.
Cite
@article{arxiv.2007.05018,
title = {Proof of modulational instability of Stokes waves in deep water},
author = {Huy Q. Nguyen and Walter A. Strauss},
journal= {arXiv preprint arXiv:2007.05018},
year = {2021}
}
Comments
A figured added to corroborate the main result numerically; to appear in Communication on Pure and Applied Mathematics