Hamiltonian Structure And Liouville Integrability Of A New Soliton Hierarchy

Starting with a new 2×2 spectral problem, a new 1+1 dimensional soliton hierarchy is presented. Then, an infinite number of conservation laws for the isospectral soliton hierarchy are deduced with the help of Riccati equations. Moreover, we prove that its 2×2 Lenard pair of operators forms a Hamiltonian pair. Thus the soliton hierarchy is the generalized Hamiltonian systems and possesses the Bi-Hamiltonian structures, Multi-Hamiltonian structrues and Liouville integrability. By using the method of derivation of functional under some constraint conditions, a complete one-to-one correspondence between the Hamiltonian functions of the hierarchy and its conservation density functions can be built. Finally, there is a gauge transformation between the spectral problem of this paper and the AKNS system. And, the potentials in these spectral problems satisfy the generalized Miura transformation, the corresponding relationship between the two soliton hierarchies is also given.