Based on a trial function method,by using two direct algebraic methods composed of hyperbolic function and triangle function,the exact solitary wave solutions and triangle function wave solutions to the nonlinear difference differential mKdV equation and Hybrid-lattice system are constructed with the help of Mathematica for the symbolic computation system.

New exact solitary wave solutions for a class of nonlinear wave equations;

New exact solitary wave solutions for nonlinear wave equation with fifth-order strong nonlinear term constructed by hyperbolic function type of auxiliary equation;

The Jacobi elliptic function exact solutions to the regular long wave equation and the mKdV equation as well as the degenerated exact solitary wave solutions are constructed with the help of symbolic computation system Mathematica.