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

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

GAO Bin^1,2, LIU Shikuo¹, FU Zuntao¹, LIU Shida¹

1. School of Physics, Peking University, Beijing 100871; 2.Department of Physics, Yuxi Normal University, Yuxi 653100;

Received:2009-04-12 Online:2009-11-20 Published:2009-11-20

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

高斌^1,2,刘式适¹,付遵涛¹,刘式达¹

1. 北京大学物理学院,北京100871; 2.玉溪师范学院物理系,玉溪653100;

Abstract

Abstract: The construction of exact solutions of nonlinear Schrdinger equations plays an important role in understanding the dynamic evolution of Bose-Einstein condensates. The Jacobi elliptic function expansion methodis appliedto 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.

Key words: Gross-Pitaevskii equation, Jacobi elliptic function, envelope periodic solution, envelope solitary solution

摘要： 非线性Schrdinger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。

关键词: Gross-Pitaevskii方程, Jacobi椭圆函数, 包络周期解, 包络孤立波解

CLC Number:

O415
O175

GAO Bin,LIU Shikuo,FU Zuntao,LIU Shida. Envelope Periodic and Solitary Solutions to One Dimensional Gross-Pitaevskii Equationin Bose-Einstein Condensates[J]. Acta Scientiarum Naturalium Universitatis Pekinensis.

高斌,刘式适,付遵涛,刘式达. Bose-Einstein 凝聚态中的一维Gross-Pitaevskii方程的包络周期解和孤立波解[J]. 北京大学学报（自然科学版）.

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

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

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