The Hamiltonian Structures And Conservation Laws For A Hierarchy Of Nonlinear Differential-Difference Equations

In this paper, we study the Hamiltonian structures and infinitely many conservation laws of Belov-Chaltikian lattice equation, which related to the discrete 3×3 matrix spec-tral problem. Starting with the matrix spectral problem (0.2), a hierarchy of nonlinear differential-difference equations which contains Belov-Chalkian as its first unform equation is proposed, with the help of the discrete zero-curvature equation. Then the Hamiltonian structures for the hierarchy are derived from the trace identity. At last, the infinitely many conservation laws of the hierarchy are obtained and the correctness was proved while m=1.