Highest Cusped Waves for the Fractional KdV Equations

Joel Dahne

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arXiv · 2308.16579

Highest Cusped Waves for the Fractional KdV Equations

Joel Dahne

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Abstract

In this paper we prove the existence of highest, cusped, traveling wave solutions for the fractional KdV equations $f_t + f f_x = |D|^{\alpha} f_x$ for all $\alpha \in (-1,0)$ and give their exact leading asymptotic behavior at zero. The proof combines careful asymptotic analysis and a computer-assisted approach.

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Joel Dahne. 2023-08-31. Highest Cusped Waves for the Fractional KdV Equations. https://arxiv.org/abs/2308.16579

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