Corpus ID: 119692201

Convexity of Whitham's highest cusped wave

  title={Convexity of Whitham's highest cusped wave},
  author={A. Enciso and Javier G'omez-Serrano and B. Vergara},
  journal={arXiv: Analysis of PDEs},
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. 
3 Citations
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