English

Generalisations of the Camassa-Holm equation

Exactly Solvable and Integrable Systems 2009-05-15 v1

Abstract

We classify generalised Camassa-Holm type equations which possess infinite hierarchies of higher symmetries. We show that the obtained equations can be treated as negative flows of integrable quasi-linear scalar evolution equations of orders 2, 3 and 5. We present the corresponding Lax representations or linearisation transformations for these equations. Some of the obtained equations seem to be new.

Keywords

Cite

@article{arxiv.0905.2219,
  title  = {Generalisations of the Camassa-Holm equation},
  author = {Vladimir Novikov},
  journal= {arXiv preprint arXiv:0905.2219},
  year   = {2009}
}