On the first bifurcation of Stokes waves
Abstract
We consider Stokes water waves on the vorticity flow in a two-dimensional channel of finite depth. In the paper "V.Kozlov, On first subharmonic bifurcations in a branch of Stokes waves, JDE, 2024," it was proved existence of subharmonic bifurcations on a branch of Stokes waves. Such bifurcations occur near the first bifurcation in the set of Stokes waves. Moreover it is shown in that paper that the bifurcating solutions build a connected continuum containing large amplitude waves. This fact was proved under a certain assumption concerning the second eigenvalue of the Frechet derivative. In this paper we investigate this assumption and present explicit conditions when it is satisfied.
Cite
@article{arxiv.2307.05573,
title = {On the first bifurcation of Stokes waves},
author = {Vladimir Kozlov},
journal= {arXiv preprint arXiv:2307.05573},
year = {2024}
}
Comments
accepted by the journal Algebra and Analysis. arXiv admin note: text overlap with arXiv:2303.11440