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Global conservative solutions of the Camassa-Holm equation for initial data nonvanishing asymptotics

Analysis of PDEs 2022-01-17 v1

Authors: Katrin Grunert , Helge Holden , Xavier Raynaud

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Abstract

We study global conservative solutions of the Cauchy problem for the Camassa-Holm equation $u_t-u_{txx}+\kappa u_x+3uu_x-2u_xu_{xx}-uu_{xxx}=0$ with nonvanishing and distinct spatial asymptotics.

Keywords

Camassa-Holm equation global conservative solutions Cauchy problem nonvanishing asymptotics integrable system shallow water waves

Cite

@article{arxiv.1106.4125,
  title  = {Global conservative solutions of the Camassa-Holm equation for initial data nonvanishing asymptotics},
  author = {Katrin Grunert and Helge Holden and Xavier Raynaud},
  journal= {arXiv preprint arXiv:1106.4125},
  year   = {2022}
}