N-soliton solutions and elastic interaction of the coupled lattice soliton equations for nonlinear waves

With the aid of symbolic computation, a coupled set of the lattice soliton equations is investigated via Darboux transformation (DT) method. The N-fold DT and conservation laws are constructed based on its Lax representation. The N-soliton solutions in terms of the Vandermonde-like determinants are derived. Structures of the one-, two-, three- and four-soliton solutions are shown graphically. Elastic interactions among the four solitons are discussed: solitonic shapes and amplitudes have not changed after the interaction. Results in this paper might be helpful for understanding the propagation of nonlinear waves.