Continuous limits for an integrable coupling of the Kac-Van Moerbeke hierarchy

In this paper, we present an integrable coupling of lattice hierarchy and its continuous limits by using Lie algebra sl(4). By introducing a complex discrete spectral problem, the integrable coupling of Kac-Van Moerbeke lattice hierarchy is derived. It is shown that a new complex lattice spectral problem converges to the integrable coupling of discrete soliton equation hierarchy, which has the integrable coupling system of MKdV hierarchy as a new kind of continuous limit.