Mixed function method for obtaining exact solution of nonlinear differential-difference equations and coupled NDDEs

In this paper, we construct a new mixed function method for the first time. By using this new method, we study the two nonlinear differential-difference equations named the generalized Hybrid lattice and two-component Volterra lattice equations. Some new exact solutions of mixed function type such as discrete solitary wave solutions, discrete kink and anti-kink wave solutions and discrete breather solutions with kink and anti-kink character are obtained and their dynamic properties are also discussed. By using software Mathematica, we show their profiles.