An estimate for the Morse index of a Stokes wave
Analysis of PDEs
2015-06-04 v2 Spectral Theory
Abstract
Stokes waves are steady periodic water waves on the free surface of an infinitely deep irrotational two dimensional flow under gravity without surface tension. They can be described in terms of solutions of the Euler-Lagrange equation of a certain functional. This allows one to define the Morse index of a Stokes wave. It is well known that if the Morse indices of the elements of a set of non-singular Stokes waves are bounded, then none of them is close to a singular one. The paper presents a quantitative variant of this result.
Keywords
Cite
@article{arxiv.1203.5811,
title = {An estimate for the Morse index of a Stokes wave},
author = {Eugene Shargorodsky},
journal= {arXiv preprint arXiv:1203.5811},
year = {2015}
}
Comments
This version contains an additional reference and some minor changes