非线性Schrdinger方程的双同宿轨道解

The doubly homoclinic orbit solution for nonlinear Schrdinger equation

在非线性动力系统中,混沌与同宿轨道的关系非常密切.关于非线性偏微分方程的单同宿轨道解已有较好的研究结果,而双同宿轨道解的研究因为其计算量大,解的形式复杂等原因并没有很好的结果.利用Hirota双线性算子方法,通过给出的相关变换,结合运用Maple软件,得到了非线性Schrdinger方程的双同宿轨道解的显示解析表达式.这种方法也可以用来求解其他具有单同宿轨道解的偏微分方程.

Chaos is closely associated with homoclinic orbits in deterministic nonlinear dynamics.There are some results about single homoclinic orbit solution for nonlinear partial differential equations.It is difficult to get doubly homoclinic orbit solution because of the large computation and the complex expression.In this paper,analytic expressions of the doubly homoclinic orbit solution for nonlinear Schrdinger equation is presented based on Hirota＇s bilinear method by a dependent variable transformation and the Maple software.This method can be used to get the doubly homoclinic orbit solutions of other partial differential equation.