Convexity of Whitham's highest cusped wave
classification
🧮 math.AP
keywords
wavewhithamconvexitycuspedhighestbeenconjecturedconsecutive
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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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