Some Investigations On Solving Exact Solution Method And Symmetry Reduction Of NLEs

There are many methods to obtain exact solutions of nonlinear evolution equa-tions(NLEs), such as Jacobi elliptic functions expansion method, Hyperbolic-Tan func-tion method, mixed power methods(混和指数法), homogenous balancing method, Hi-rota method, inverse scattering method, Backlund transformation method, etc., inwhich Hyperbolic-Tan function method is one of the best efficient methods. Eachmethod of mentioned above has its own advantages to solve exact solutions of NLEs.The different methods are suitable for different class of evolution equations.In this paper, we discuses a method of solving exact solutions of NLEs and itssymmetry reductions.Firstly, we give a concept of rank for NLEs and use it treating the equations indifferent classes. For each class we give a pre-judge to use appropriate method. Insolving exact solutions of NLEs we first make a transformation of traveling reduce theequation to a ordinary differential equation, then using Jacobi elliptic functions expan-sion method and a modified Hyperbolic- Tan function method, we successfully solvethe exact solution of KdV equation, MKdV-Burgers equation, Joseph- Egri equation.Secondly, using the properties of Lie groups of a partial differential equationsmaking the equations invariance, we reduce KdV equation, Joseph- Egri equation,Boussinesq equations, mBBM equation and Fujimoto- Watanabe equation to ordinarydifferential equation (equations), which provides one more convenience to solve theseequations by various methods.Mainly Hyperbolic- Tan function method, homogeneous balancing method, Math-ematica software and wu's method play key rules in our obtained results.