A nonisospectral extension of the Volterra hierarchy to 2+1 dimensions

We give a new nonisospectral generalization of the Volterra lattice equation to 2+1 dimensions. We use this to construct a new nonisospectral lattice hierarchy in 2+1 dimensions, along with its underlying linear problem. Reductions yield a variety of new integrable hierarchies, including generalizations of known discrete Painlevé hierarchies, all along with their corresponding linear problems. This represents an extension of previously developed techniques to the discrete case.