Two New Integrable Lattice Hierarchies Associated With A Discrete Schrodinger Nonisospectral Problem and Their Infinitely Many Conservation Laws

Abstract

In this article, by means of using discrete zero curvature representation and constructing opportune time evolution problems, two new discrete integrable lattice hierarchies with n-dependent coefficients are proposed, which related to a new discrete Schr\"{o}dinger nonisospectral operator equation. The relation of the two new lattice hierarchies with the Volterra hierarchy is discussed. It has been shown that one lattice hierarchy is equivalent to the positive Volterra hierarchy with n-dependent coefficients and another lattice hierarchy with isospectral problem is equivalent to the negative Volterra hierarchy. We demonstrate the existence of infinitely many conservation laws for the two lattice hierarchies and give the corresponding conserved densities and the associated fluxes formulaically. Thus their integrability is confirmed.