Integrable lattice hierarchies associated with two new (2+1)-dimensional discrete spectral problems

In this Letter, by considering two new (2+1)-dimensional discrete linear spectral problems, new (2+1)-dimensional integrable lattice hierarchies are constructed. It is shown that the two new (2+1)-dimensional integrable lattice hierarchies are extensions (to nonisospectral and (2+1)-dimensional cases) of a (1+1)-dimensional 3-field lattice hierarchy of Zhang et al. and a (1+1)-dimensional 2-field lattice hierarchy due to Merola, Ragnisco and Tu. We also obtain new (1+1)-dimensional nonisospectral lattice hierarchies which include a nonisospectral relativistic Toda lattice hierarchy.