联立薛定谔方程的不传播光孤子和传播光孤子

The Nonpropagating Light Soliton and Propagating Light Soliton for the Simultaneous Schrdinger Equation

映射法是一种非常经典、有效而且非常成熟的一种求解非线性演化方程的方法,其最大的特点是可以有无穷多个不同形式的设解,使得最终求得的解丰富多彩。传统的方法是在行波约化的前提下,即在常微分方程下进行映射。将这种方法进行扩展,推广成变系数的非行波约化下的映射,取得了成功,并利用改进的里卡蒂(Riccati)方程映射法,得到了联立薛定谔方程(负KdV方程)新的精确解。根据所得到的解模拟出了联立薛定谔方程的不传播光孤子(时间光孤子和亮-暗脉冲光孤子)和传播光孤子,以及光孤子的中和现象。

The mapping approach is a kind of classic, efficient and well-developed method to solve nonlinear evolution equations, the remarkable characteristics of which is that we can have infinitely different ansatzs and thus end up with the abundance of solutions. The traditional ways are to map on the basis of travelling wave reduction, i. e., on the basis of ordinary differential equations. Recently, we have successfully extended this method to the mapping on the variable-coefficients non-traveling wave reduction. Using an improved Riccati mapping approach, we obtain new exact solutions for the （1＋1）-dimensional related to Schrodinger equation. Based on the derived solutions, the nonpropagating light solitons（temporal light soliton and bight-dark pulse light soliton）, propagating light solitons, and the neutralisation phenomena of light-solitons were constructed.