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arXiv · 2307.05573

On the first bifurcation of Stokes waves

Vladimir Kozlov
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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.

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Vladimir Kozlov. 2023-07-10. On the first bifurcation of Stokes waves. https://arxiv.org/abs/2307.05573

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