一类非线性薛定谔方程的孤子解

 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.

Soliton solution of certain nonlinear Schrodinger equation

The one-soliton solution of the nonlinear Schrdinger equation with an external potential of the form of V(x,t) =f₁(t)x+f₂(t)x² 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 f₁(t).In principle,the soliton can be diffused if f₂(t) varies rapidly.Through numerical method,however,that the soliton is extremely tenacious against rapid variations of f₂(t).