Proof of Modulational Instability of Stokes Waves in Deep Water

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....

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Bibliographic Details
Published inCommunications on pure and applied mathematics Vol. 76; no. 5; pp. 1035 - 1084
Main Authors Nguyen, Huy Q., Strauss, Walter A.
Format Journal Article
LanguageEnglish
Published Melbourne John Wiley & Sons Australia, Ltd 01.05.2023
John Wiley and Sons, Limited
Subjects
Deep water
Perturbation
Stability
Water waves
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Summary: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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ISSN:0010-3640
1097-0312
DOI:10.1002/cpa.22073