English

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

Analysis of PDEs 2021-01-01 v1

Abstract

The well-known Stokes waves refer to periodic traveling waves under the gravity at the free surface of a two dimensional full water wave system. In this paper, we prove that small-amplitude Stokes waves with infinite depth are nonlinearly unstable under long-wave perturbations. Our approach is based on the modulational approximation of the water wave system and the instability mechanism of the focusing cubic nonlinear Schr\"odinger equation.

Keywords

Cite

@article{arxiv.2012.15071,
  title  = {Nonlinear modulational instabililty of the Stokes waves in 2d full water waves},
  author = {Gong Chen and Qingtang Su},
  journal= {arXiv preprint arXiv:2012.15071},
  year   = {2021}
}