(2+2)-Dimensional Discrete Soliton Equations and Integrable Coupling System

In this paper, we extend a (2+2)-dimensional continuous zero curvature equation to (2+2)-dimensional discrete zero curvature equation, then a new (2+2)-dimensional cubic Volterra lattice hierarchy is obtained. Furthermore, the integrable coupling systems of the (2+2)-dimensional cubic Volterra lattice hierarchy and the generalized Toda lattice soliton equations are presented by using a Lie algebraic system sl(4). (general)