Abstract
AbstractIt 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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