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

Abstract: In this paper, we present an integrable coupling of lattice hierarchy and its continuous limits by using Lie algebra . 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. [Copyright &y& Elsevier]