Generalisations of the Camassa-Holm equation

Details Generalisations of the Camassa-Holm equation Generalisations of the Camassa-Holm equation

2009-05-13

arxiv.org/abs/0905.2219v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Scientific paper

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.

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