On the first bifurcation of solitary waves
Analysis of PDEs
2023-11-28 v1 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.2311.15336,
title = {On the first bifurcation of solitary waves},
author = {Vladimir Kozlov},
journal= {arXiv preprint arXiv:2311.15336},
year = {2023}
}
Comments
arXiv admin note: text overlap with arXiv:2307.05573, arXiv:2303.11440