The Generalized Camassa-Holm Hierarchy and Its Solution

Abstract:
A generalized Camassa-Holm hierarchy is presented and this hierarchy is proved to be integrable in the sense of Lax pair. The relation between the PDE hierarchy and the constrained Hamiltonian system is discussed. A 3– by– 3 spectral problem and its adjoint problem are introduced. Furthermore, the solutions for the whole
hierarchy are obtained.