利用玻色-费米图像,发现了一维Tonks-Girardeau气体的孤子解,方法是在平均场近似的基础上,利用对称变换,将GP方程转化为高阶强相互作用的非线性薛定谔方程,之后解析求解这个含五次方的非线性薛定谔方程,得到一个亮孤子解,这对从实验上观测Tonks-Girardeau气体的孤子现象具有指导作用.
Base on spherical symmetric trap treatment, we analyze how to change a generalized Gross-Pitaevskii equation to a quintic nonlinear Sehroedinger equation. Analysing the nonlinear Sehroedinger equation, we find a typical bright soliton solution in Tonks- Girardeau gas region. This will help experimental observations.