对称在破裂孤立子方程中的应用

Application of symmetry in breaking soliton equation

首先对带有积分项的破裂孤立子方程(breaking soliton equation)进行变换,然后利用待定系数法求出它的对称,通过验证知道原方程的李群能构成李代数,再利用优化系统对原方程进行约化,求出了原方程的一些新解。

In this paper we first make transform to the breaking soliton equation which has an integration term,then obtain the symmetries of the equation by using the Lie group method and verify that the corresponding vector field can constitute Lie algebra. We also get some reduced forms of the breaking soliton equation with the ad joint presentation.We obtain some new solutions of the breaking soliton equation in the end.