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arXiv · 1709.02330

Singularities of Whitham flows for hyperelliptic spectral curves

Laurent Hauswirth·Martin Kilian·Martin U. Schmidt
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Abstract

We consider the Whitham equations for deformations of hyperelliptic spectral curves, which preserve all periods of a meromorphic differential. If the meromorphic differential has a root at a fixed point of the hyperelliptic involution, then the Whitham flow has a singularity. We prove that the stable and unstable manifolds are non-empty and extend the Whitham flow continuously through the singularity.

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Laurent Hauswirth, Martin Kilian, Martin U. Schmidt. 2017-09-08. Singularities of Whitham flows for hyperelliptic spectral curves. https://arxiv.org/abs/1709.02330

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