Highest Cusped Waves for the Fractional KdV Equations

Joel Dahne

Highest Cusped Waves for the Fractional KdV Equations

Analysis of PDEs 2023-09-01 v1

Authors: Joel Dahne

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.

Keywords

traveling waves

Cite

@article{arxiv.2308.16579,
  title  = {Highest Cusped Waves for the Fractional KdV Equations},
  author = {Joel Dahne},
  journal= {arXiv preprint arXiv:2308.16579},
  year   = {2023}
}

Comments

86 pages, 6 figures

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