一类非线性薛定谔方程的孤子解  

Soliton solution of certain nonlinear Schrdinger equation

作　　者：刘良桂[1] 李云德[1] 

机构地区：[1]云南大学物理系,云南昆明650091

出　　处：《云南大学学报（自然科学版）》2004年第2期132-133,138,共3页Journal of Yunnan University(Natural Sciences Edition)

基　　金：国家自然科学基金资助项目(10347011).

摘　　要：研究了具有V(x,t)=f1(t)x+f2(t)x2形式的外部势的非线性薛定谔方程的单一孤立子解.结果表明:当孤立子的中心满足带有势V(x,t)的牛顿方程,孤立子的内部结构由"体固定"坐标系决定.孤立子的结构与f1(t)无关.若f2(t)与t无关,孤立子是固定的.原则上,若f2(t)剧烈变化,则孤立子将扩散.但数值计算表明,在一定条件下,孤立子还是经得起f2(t)的剧烈变化.The one-soliton solution of the nonlinear Schrdinger equation with an external potential of the form of V(x,t)=f_1(t)x+f_2(t)x^2 is examined.It is shown that,while the center of the soliton obeys Newton's equation with the potential V(x,t) ,the internal structure of the soliton is determined by the NLSE of the 'body-fixed' coordinate system.The soliton structure is found to be independent of f_1(t) .In principle,the soliton can be diffused if f_2(t) varies rapidly.Through numerical method,however,that the soliton is extremely tenacious against rapid variations of f_2(t) .

关 键 词：非线性薛定谔方程 孤子解 玻色-爱因斯坦凝聚 牛顿方程 

分 类 号：O413[理学—理论物理] O411.1[理学—物理]