New Exact Solutions Of Several Nonlinear Evolution Equations

In order to obtain new exact solutions of nonlinear evolution equations,on the basis of essays studying auxiliary equation method and the directmethod-CK method. We improve auxiliary equation method and the directmethod, and construct new exact solution for several nonlinear evolutionequations with the help of symbolic computation system Mathematica.In the first chapter we introduce the generation and development ofsoliton conception, the history of the method for solving nonlinear evolutionequations and the main work.In the second chapter, we structure exact solution of nonlinear evolutionequations by using the auxiliary equation method.(1) Obtain a hyperbolicfunction solutions and trigonometric function solutions of a two-orderordinary differential equations that we give, and construct the exact solutionof the constant coefficient nonlinear evolution equations.(2) Third-orderlinear homogeneous ordinary differential equations, construct new exactsolution of (2+1)-dimensional modified dispersive water-wave systemincluding composite exact solution of a combination of trigonometric andexponential functions, and a combination of rational function and exponentialfunction.(3) By using the method of Riccati equations, we construct exactsolutions of soliton of several variable coefficient nonlinear evolution equations.In the third chapter, through B cklund transformation formulas of thevariable coefficients (2+1)-dimensional Broer-Kaup equation that is obtainedby making use of the direct method-CK method, constructe new exactsolutions of the variable coefficients (2+1)-dimensional Broer-Kaup equation.