一维Tonks-Girardeau原子气区域中Gross-Pitaevskii方程简化模型的无穷序列新解  

New infinite sequence solutions for simplified model of GP equation in 1D-Tonks-Girardeau gas

作　　者：阿如娜[1] 套格图桑[1] 

机构地区：[1]内蒙古师范大学数学科学学院,内蒙古呼和浩特010022

出　　处：《量子电子学报》2014年第5期541-546,共6页Chinese Journal of Quantum Electronics

基　　金：国家自然科学基金资助项目(11361040);内蒙古自治区高等学校科学研究基金(NJZY12031);内蒙古自治区自然科学基金(2010MS0111)资助

摘　　要：人们一直以来对于含五次方的一维非线性薛定谔方程的求解问题感兴趣,但是只获得了由椭圆函数和双曲函数组成的有限多个新解。为了获得含五次方的一维非线性薛定谔方程的无穷序列新解,对该方程进行了一系列变换,从而利用RIccati方程的Backlund变换和解的非线性叠加公式等相关结论,构造了含五次方的一维非线性薛定谔方程的由三角函数、双曲函数和有理函数组成的无穷序列新精确解。People are always interested in solving the problem of one-dimensional nonlinear Schr5dinger equation with the fifth power. However, only a limited number of new solutions consisting of the elliptic and hyperbolic functions were obtained. In order to obtain a new infinite sequence solutions of one-dimensional nonlinear SchrSdinger equation with fifth power, it makes a series of transformations on the equation, and using the related conclusions of B^cklund transform and nonlinear superposition formula of Riccati equation the new infinite sequence solutions of one-dimensional nonlinear SchrSdinger equation with the fifth power consisting of trigonometric function, hyperbolic function and rational function were constructed.

关 键 词：非线性方程 GROSS-PITAEVSKII方程 RICCATI方程 非线性叠加公式 无穷序列新解 

分 类 号：O175.29[理学—数学]