Abstract
We construct nonlinear integrable couplings of discrete soliton hierarchy, then the infinite conservation laws for the nonlinear integrable couplings of the lattice hierarchy are established. For explicit application of the method proposed, the infinite conservation laws of nonlinear integrable couplings of the Toda lattice hierarchy are presented. The obtained integrable couplings of the Toda lattice equations and conservation laws can be used to describe the possible formation mechanisms for hydrodynamics, solid state physics and plasma physics, respectively.
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