Analytical Solutions for the Two-Dimensional Gross?Pitaevskii Equation with a Harmonic Trap
Analytical Solutions for the Two-Dimensional Gross?Pitaevskii Equation with a Harmonic Trap
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DOI：
10.1088/0253-6102/59/3/05
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发表时间：
2013-03
影响因子：
3.1
通讯作者：
Yu-Ren Shi;Xue-Ling Wang;Guang-Hui Wang;Cong-Bo Liu;Hong-juan Yang
中科院分区：
文献类型：
--
作者：
Yu-Ren Shi;Xue-Ling Wang;Guang-Hui Wang;Cong-Bo Liu;Hong-juan Yang
本文应用同伦分析方法和伽辽金谱方法，求出二维时无关的Gross-Pitaevskii方程的解析解。Gross-Pitaevskii方程是描述玻色-爱因斯坦凝聚体被困在谐波势中的非线性薛定谔方程。成功地得到了近似解析解。并对解析解和数值解进行了比较。结果表明，在原子相互作用不太强的情况下，它们是非常吻合的。
Both the homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions of the two-dimensional and time-independent Gross-Pitaevskii equation, a nonlinear Schrodinger equation used in describing the system of Bose-Einstein condensates trapped in a harmonic potential. The approximate analytical solutions are obtained successfully. Comparisons between the analytical solutions and the numerical solutions have been made. The results indicate that they are agreement very well with each other when the atomic interaction is not too strong.