含微扰Sine-Gordon方程的代数解法

AN ALGEBRIC APPROACH FOR THE PERTURBED SINE-GORDON EQUATION

本文采用一种新的方法研究单原子吸附的非线性动力学方程.将含微扰的Siue-Gordon方程转化为代数方程,进一步求得Sine-Gordon方程的解.该解的特点是当微扰为零时,结果与Sine-Gordon方程的标准解一致;微扰项的影响使解的对称性破缺,且破缺程度的大小随着微扰的增加而增大。

A new approach is developed in discussing the nonlinear dynamical equation of an absorbed atom. The perturbed Sine-Gordon equaton is transformed to an algebric equation, and we obtain the soliton solution of it. The characteristic of the solution is the symme- try breaking for a kink and antikink soliton. The influence of the per- turbed term on the solution is more evident as the increase of the per- turbed parameter.