In the paper,with the aid of computer algebraic system Mathematica or Maple 10,the extended hyperbolic function method was used in order to seek for exact soliton solutions and exact travel wave solutions of the modified forms of Camassa-Holm and Degasperis-Procesi Equations,more new exact soliton solutions and exact travel wave solutions are found by means of this method.

An exact soliton solutions to the equation is derived by using the extended homogeneous balance method and the truncated expansion method.

By using a simple transformation and constructing auxiliary equation,the exact soliton solutions for a class KdV system are obtained and the properties of the solutions are also discussed.

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.

In this paper,some methods of solving the exact isolated wave solution of nonlinear evolution equation with higher-dim ension were developed and the exactisolated wave solutions of Kundu equation and PC equation with higher-dim ension were given.