Generalizations of the Camassa–Holm equation

Abstract

We classify generalized 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 linearization transformations for these equations. Some of the obtained equations seem to be new.

Identifiers

DOI

10.1088/1751-8113/42/34/342002

Citations and references