Bose-Einstein凝聚态中的一维Gross-Pitaevskii方程的包络周期解和孤立波解

Envelope Periodic and Solitary Solutions to One Dimensional Gross-Pitaevskii Equation in Bose-Einstein Condensates

非线性Schr dinger方程的精确解对于理解Bose-Einstein凝聚态动力学演化有重要的作用。应用Jacobi椭圆函数展开法,求得描述Bose-Einstein凝聚态的一维Gross-Pitaevskii方程的包络周期解。在极限情况下,包络周期解可导出包络孤立波解。

The construction of exact solutions of nonlinear Schrdinger equations plays an important role in understanding the dynamic evolution of Bose-Einstein condensates.The Jacobi elliptic function expansion method is applied to construct the envelope periodic solutions to one dimensional Gross-Pitaevskii equation in Bose-Einstein condensates.The envelope periodic solutions can degenerate to the envelope solitary solutions under the limited condition.