A Hierarchy Of Generaled Coupled Harry-dym Equations And Their Hamiltonian Structures And Decomposition

A 4×4 matrix spectral problem with two potentials is introduced, by which a hierarchy of generalized coupled Harry-Dym equations and their bi-Hamiltonian structures are derived. With the help of the nonlinearization approach of Lax pairs, the generalized coupled Harry-Dym equations are decomposed into two compatible finite-dimensional Hamiltonian systems.