Analytic solutions and Darboux transformation to a new Hamiltonian lattice hierarchy

Abstract

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 [Formula: see text], 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.