On the first bifurcation of solitary waves

Vladimir Kozlov

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arXiv · 2311.15336

On the first bifurcation of solitary waves

Vladimir Kozlov

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Abstract

We consider solitary water waves on the vorticity flow in a two-dimensional channel of finite depth. The main object of study is a branch of solitary waves starting from a laminar flow and then approaching an extreme wave. We prove that there always exists a bifurcation point on such branches. Moreover, the crossing number of the first bifurcation point is 1, i.e. the bifurcation occurs at a simple eigenvalue.

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Vladimir Kozlov. 2023-11-26. On the first bifurcation of solitary waves. https://arxiv.org/abs/2311.15336

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