Darboux transformation and soliton solutions of a nonlinear coupled differential-difference equation

In this paper, a coupled nonlinear differential-difference equation is investigated by the Lax theory and Darboux transformation (DT) technique. The new Lax pair of that system is constructed. Based on the resulting Lax pair, a new DT with two variable parameters is constructed and established. Explicit one-soliton solutions are derived via the DT. Structure figures of the one-soliton solutions are shown graphically.