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arXiv · 1810.10935

Convexity of Whitham's highest cusped wave

Alberto Enciso·Javier Gómez-Serrano·Bruno Vergara
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Abstract

We prove the existence of a periodic traveling wave of extreme form of the Whitham equation that has a convex profile between consecutive stagnation points, at which it is known to feature a cusp of exactly $C^{1/2}$ regularity. The convexity of Whitham's highest cusped wave had been conjectured by Ehrnstr\"om and Wahl\'en.

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Alberto Enciso, Javier Gómez-Serrano, Bruno Vergara. 2018-10-25. Convexity of Whitham's highest cusped wave. https://arxiv.org/abs/1810.10935

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