Hamiltonian Structure And Conservation Laws Of The Modified Belov-Chaltikian Lattice Hierarchy

In this paper,we mainly study the infinite conservation laws and Hamiltonian structures of the modified Belov-Chaltikian lattice hierarchy of nonlinear differential-difference equation.In order to achieve this,we need to use some formulas in the derivation process of the modified Belov-Chaltikian lattice hierarchy,so the first part of this paper reviews the derivation of the lattice hierarchy.A discrete 3 × 3 matrix spectral problem with two potentials is firstly introduced,Then the lattice hierarchy are derived by means of the auxiliary problem and the stationary discrete zero-curvature equation.Immediately,the Riccati equation is obtained from Lax pair.Resorting to the solution of the Riccati equation,the infinitely many conservation laws of the hierarchy are gained.Finally,the Hamiltonian structure of modified Belov-Chaltikian lattice hierarchy is solved by using the trace identity.