含时线性势Gross-Piteavskii方程的孤立波解  

Exact solitary wave solutions for the Gross-Piteavskii equation with time-dependent linear potential

作　　者：石玉仁[1] 许新建[1] 吴枝喜[1] 汪映海[1] 杨红娟[2] 吕克璞[2] 段文山[2] 

机构地区：[1]兰州大学理论物理研究所,甘肃兰州730000 [2]西北师范大学物理与电子工程学院,甘肃兰州730070

出　　处：《兰州大学学报（自然科学版）》2007年第4期131-135,共5页Journal of Lanzhou University(Natural Sciences)

基　　金：国家自然科学基金(10247008).

摘　　要：首先对双曲函数法进行了扩展,使其可用于求解变系数非线性演化方程,然后用此方法成功得到了Gross-Pitaevskii方程在某含时线性势下的两类精确解.结果表明在吸引势情形下,方程存在钟形包络孤立波解;在排斥势情形下,存在扭结形包络孤立波解.该方程可用来描述重力场中在随时间变化的外磁场作用下的玻色—爱因斯坦凝聚体的演化过程,故所得解具有重要的物理意义.We extended the hyperbolic function method for solving the nonlinear evolution equations with variable coefficients. By using this method, we derived two types of exact solutions to the Gross-Pitaevskii equation with time-dependent linear potential. The results indicated that the equation has bell-like envelope solution when the potential is attracted while it has kink envelope solution when the potential is repelled. Because the Gross-Pitaevskii equation can be used to describe the process of Bose-Einstein condensation in gravity field and magnetic field, the solutions we obtained are physically important.

关 键 词：Gross-Piteavskii方程 扩展双曲函数法 精确解 孤立波解 

分 类 号：O411.1[理学—理论物理] O175.2[理学—物理]