English

The Benjamin-Feir instability in the infinite depth

Analysis of PDEs 2021-02-18 v3 Pattern Formation and Solitons Fluid Dynamics

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.

Keywords

Cite

@article{arxiv.2009.01593,
  title  = {The Benjamin-Feir instability in the infinite depth},
  author = {Vera Mikyoung Hur},
  journal= {arXiv preprint arXiv:2009.01593},
  year   = {2021}
}

Comments

There was an error in Section 6

R2 v1 2026-06-23T18:17:28.331Z