Carr L D, Kutz J N, Reinhardt W P
Department of Physics, University of Washington, Seattle, Washington 98195-1560, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Jun;63(6 Pt 2):066604. doi: 10.1103/PhysRevE.63.066604. Epub 2001 May 18.
The cubic nonlinear Schrödinger equation is the quasi-one-dimensional limit of the mean-field theory which models dilute gas Bose-Einstein condensates. Stationary solutions of this equation can be characterized as soliton trains. It is demonstrated that for repulsive nonlinearity a soliton train is stable to initial stochastic perturbation, while for attractive nonlinearity its behavior depends on the spacing between individual solitons in the train. Toroidal and harmonic confinement, both of experimental interest for Bose-Einstein condensates, are considered.
立方非线性薛定谔方程是模拟稀薄气体玻色 - 爱因斯坦凝聚体的平均场理论的准一维极限。该方程的定态解可表征为孤子列。结果表明，对于排斥性非线性，孤子列对初始随机微扰是稳定的，而对于吸引性非线性，其行为取决于孤子列中各个孤子之间的间距。还考虑了环形约束和谐波约束，这两者在玻色 - 爱因斯坦凝聚体的实验中都具有重要意义。
