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arXiv · 2201.13159

Highest waves for fractional Korteweg--De Vries and Degasperis--Procesi equations

Magnus C. Ørke
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Abstract

We study traveling waves for a class of fractional Korteweg--De Vries and fractional Degasperis--Procesi equations with a parametrized Fourier multiplier operator of order $-s \in (-1, 0)$. For both equations there exist local analytic bifurcation branches emanating from a curve of constant solutions, consisting of smooth, even and periodic traveling waves. The local branches extend to global solution curves. In the limit we find a highest, cusped traveling-wave solution and prove its optimal $s$-H\"older regularity, attained in the cusp.

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Magnus C. Ørke. 2022-01-31. Highest waves for fractional Korteweg--De Vries and Degasperis--Procesi equations. https://arxiv.org/abs/2201.13159

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