paper

Convexity of Whitham's highest cusped wave

arXiv:1810.10935

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 regularity. The convexity of Whitham's highest cusped wave had been conjectured by Ehrnström and Wahlén.

32 pages, preliminary version