Constructing exact solutions to differential-difference equations via the coupled Riccati equations
利用耦合的Riccati方程组构造微分-差分方程精确解

An algebraic method to construct the exact solutions of nonlinear differential-difference equations is presented by introducing the coupled Riccati equations. As an example, we apply this method to the general lattice equation, the relativistic Toda lattice equations and the (2+1) dimensional Toda lattice equation. Some kink solitary wave solutions and complexiton solutions are obtained with the help of symbolic system Mathematica. Our method can also be applied to other nonlinear differential-difference equations.