中文摘要：

为有效实现全光控制,基于非线性薛定谔方程（NLSE）,对势阱调制下的非线性系统中的空间光孤子的形成及其属性进行了理论研究。运用分离变量法,求出二维无限深势阱调制下的（2＋1）维变系数NLSE的精确孤子解;在此基础之上,对亮空间光孤子的的几何结构和空间分布进行研究,发现经二维无限深势阱调制后形成的椭圆形状孤子簇呈现出链状结构或矩阵结构。研究结果表明,势阱量子数、宽度等系统参数对亮空间光孤子的空间分布存在影响,通过调节参数可以有效实现全光控制。

英文摘要：

The existence and characteristics of spatial solitons in the nonlinear system,modulated by infi- nite potential trap and described by the nonlinear Schr 鰀 inger equation,are investigated theoretically in order to realize all-optical control effectively. An analytical study of the nonlinear Schr 鰀 inger equation has been of great interest for decades. The （2＋1）-dimensional nonlinear Schr 鰀 inger equation with va- rying coefficients is solved by means of a developed method of separation of variables,and the exact soli- ton solutions are obtained. We find that the elliptical soliton clusters modulated by two-dimensional infi- nite potential trap show chain or matrix structure. It is indicated that the spatial distribution of spatial solitons modulated by two-dimensional infinite potential trap depends on the quantum numbers and the width of the potential trap. By adjusting the above-mentioned parameters, all-optical control can be a- chieved effectively. The results can be of significance usefulness for the explanation of some special phys- ical problems.