Recursion operators and conservation laws for discrete Lax equations

In this paper, a method for constructing recursion operator of discrete Lax equations is proposed. To illustrate the method, recursion operators for discrete Boussinesq equation and discrete KdV equation are obtained. Then the recursion operators of continuous Boussinesq equation and KdV equation are successfully recovered by the discrete ones. Infinitely many conservation laws of discrete Boussinesq equation are constructed by the discrete residue formula and the first three conserved quantities are given explicitly and verified numerically. Existence of recursion operators and infinite number of conservation laws proves the integrability of the discrete Lax equations.