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

摘要

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.