Proof of Modulational Instability of Stokes Waves in Deep Water
Huy Q. Nguyen, Walter A. Strauss
Source abstract
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. © 2022 Courant Institute of Mathematics and Wiley Periodicals LLC.
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