An expanded G´/G-expansion method for nonlinear lattice equations

Lattice models are associated with rather important problems in physics. Solution of these models gives insights into the nature of phase transitions, magnetization and scaling behavior, as well as insights into the nature of quantum field theory. An expanded G´/G-expansion method is presented to seek explicit solutions of nonlinear lattice equations. The key steps of the expanded method is illustrated. With the aid of symbolic computation, the general mKdV lattice equation is chosen to show the validity and advantages of the method. As a result, hyperbolic function solutions and trigonometric function solutions with parameters are obtained. The proposed algorithm can be used for many other nonlinear lattice equations in mathematical physics.