The Benjamin-Feir instability in the infinite depth

Abstract

We prove that a Stokes' periodic wave of sufficiently small amplitude, traveling under gravity at the free surface of a two dimensional, infinitely deep, and irrotational flow, is spectrally unstable to slow modulation, rigorously justifying Benjamin and Feir's formal argument.

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Cited by in corpus (1)

• Nonlinear modulational instabililty of the Stokes waves in 2d full water waves