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}
}