The Study On Solving Nonlinear Evolution Equations

This paper studies mainly the exact solutions of nonlinear evolution equations, Backlund transformation , Darboux transformation and the complexion solutions of nonlinear evolution equations in soliton theory .The new-type Darboux transformation of variable coefficients KdV equation is given by use of the Painleve expansion of variakle coefficients KdV equation in the first chapter.In the second chapter,the auto-Backlund transformation and the new-type exact solitary wave solution of (2+1) dimensional breaking solution equation and the new-type exact solitary wave solutions of (2+1) dimensional dispersire long wave equation are constructed by using the truncated Painleve expansion method .The new-type soliton-like solutions of (2+1)- dimensional dispersive long wave equation and (2+1) dimensional Broer-Kaup equation are derived by using the homogeneous balance method in the third chapter.In the fourth chapter, the complexion solutions which expressed by Wronskian determinant of the CDGKES equation and the KP equation are presented.