Symmetry Analysis Of Several Nonlinear Differential Equations

In this paper,we mainly study the symmetry analysis of several nonlinear differential equations.With the aid of Maple,we obtain the symmetry transformation of a(2+1)-dimensional differential-difference equation baced on the Lou's direct method.Moreover,a new soliton-like solution and numerical examples of the differential-difference equation is presented based on the symmetry transformation.And we use the classical Lie group method to solve the symmetry reductions of the nonisospectral Lax pair for a(2+1)-dimensional breaking soliton equation and its Lax pair by considering the spectral parameter as an additional field.Then we give new reduced equations with their nonisospectral or isospectral Lax pairs.Through the comparison of the reduced equation and reduced Lax pair on the compatibility conditions,we found that the reduced Lax pair is the Lax pair of the reduced equations exactly.And through a reduced Lax pair,we obtain an explicit solution of the breaking soliton equation.The plan of this paper is as follows.In the introduction,we introduce the history and development of integrable system and soliton theory.Meanwhile,the solving methods and symmetry analysis of nonlinear differential equations are also described.The second chapter and the third chapter are the main contents of the article.And the summary is given at the end of the paper.