Hamiltonian Structures and Reciprocal Transformations for the $r$-KdV-CH Hierarchy

Ming Chen, Si-Qi Liu, Youjin Zhang

The $r$-KdV-CH hierarchy is a generalization of the Korteweg-de Vries and Camassa-Holm hierarchies parametrized by $r+1$ constants. In this paper we clarify some properties of its…