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.