Continuous limits for an integrable coupling system of Toda equation hierarchy

Abstract: In this Letter, we present an integrable coupling system of lattice hierarchy and its continuous limits by using of Lie algebra . By introducing a complex discrete spectral problem, the integrable coupling system of Toda lattice hierarchy is derived. It is shown that a new complex lattice spectral problem converges to the integrable couplings of discrete soliton equation hierarchy, which has the integrable coupling system of C-KdV hierarchy as a new kind of continuous limit. [Copyright &y& Elsevier]