Analytic solutions and Darboux transformation to a new Hamiltonian lattice hierarchy

In this paper, a new Hamiltonian lattice hierarchy is analytically investigated, which can be reduced to some classic integrable lattice hierarchies, such as Ablowitz-Ladik hierarchy, Volterra hierarchy and multi-Hamiltonian lattice hierarchy, etc. By choosing the auxiliary problem V-n((m)), n, we present a Darboux transformation (DT) to the new discrete matrix spectral problem. As its applications, a series of analytical solutions are generated in a recursive manner. Finally, the graphical analysis of these analytical solutions are presented, respectively. The DT of other lattice hierarchies can be also constructed in this method.