Symmetrical About Nonlinear Evolution Equations Calculated Precisely And Reduced

The main content of the paper is to solve the nonlinear evolution equation whichis one of the most important problems in the soliton theory and in the application.This paper also introduces some effective solving methods. By the application of themand their improved methods, some new exact solutions are presented.Chapter1is devoted to reviewing the history and development of the solitontheory and the solving methods which can solve the nonlinear evolution equations.My topic selection and main works are listed at last.Chapter2is based on the idea of algebraic method and algorithm realization forsolving nonlinear evolution equations. With the help of symbolic computation system,the uniform algebraic method can be used to construct a variety of periodic solutions.New exact solutions of (2+1) dimension Caudery-Dodd-Gibbon equation arepresented by using Weierstrass elliptic function, Riccati equation and Jacobi ellipticfunction.In Chapter3, the properties of the bilinear operator, the transformations to getbilinear equation and bilinear method are introduced firstly. Logarithmic andB cklundtransformation are obtained by using Painlev étruncated expansionmethod, which can be used to transform (2+1) dimension Caudery-Dodd-Gibbonequation into bilinear equation. At last, soliton solutions are presented.Chapter4respectively introduces the reduced-order and reduced-dimension effectof Lie symmetry methods to solve ordinary differential equations and partialdifferential equations. It also introduces invariant variable method. Then the reducedequation and group-invariant solutions of (2+1) dimension Caudery-Dodd-Gibbonequation and (2+1) dimension Harry-Dym equation are obtained by this method. Atlast, parameter hypothesis is introduced to obtain Lie symmetry, and the symmetry of(2+1) dimension Harry-Dym equation is obtained.