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arXiv · 1303.6721

Global bifurcation for the Whitham equation

Mats Ehrnstrom·Henrik Kalisch
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Abstract

We prove the existence of a global bifurcation branch of $2π$-periodic, smooth, traveling-wave solutions of the Whitham equation. It is shown that any subset of solutions in the global branch contains a sequence which converges uniformly to some solution of Hölder class $C^α$, $α< \frac{1}{2}$. Bifurcation formulas are given, as well as some properties along the global bifurcation branch. In addition, a spectral scheme for computing approximations to those waves is put forward, and several numerical results along the global bifurcation branch are presented, including the presence of a turning point and a `highest', cusped wave. Both analytic and numerical results are compared to traveling-wave solutions of the KdV equation.

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Mats Ehrnstrom, Henrik Kalisch. 2013-03-27. Global bifurcation for the Whitham equation. https://arxiv.org/abs/1303.6721

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