Homoclinic Orbits for a Perturbed Lattice Modified KdV Equation

We establish the splitting of homoclinic orbits for a near-integrable lattice modified KdV (mKdV) equation with periodic boundary conditions. We use the Bäcklund transformation to construct homoclinic orbits of the lattice mKdV equation. We build the Melnikov function with the gradient of the invariant defined through the discrete Floquet discriminant evaluated at critical points. The criteria for the persistence of homoclinic solutions of the perturbed lattice mKdV equation are established.