Gross-Pitaevskii方程的新解  

New Solutions of Gross-Pitaevskii Equation

作　　者：白玉梅[1] 套格图桑[1,2] 

机构地区：[1]内蒙古民族大学数学学院,内蒙古通辽028043 [2]内蒙古师范大学数学科学学院,呼和浩特010022

出　　处：《内蒙古大学学报（自然科学版）》2015年第6期574-581,共8页Journal of Inner Mongolia University：Natural Science Edition

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资助(NJZY12031);内蒙古自治区自然科学基金资助(2015MS0128)

摘　　要：通过下列步骤,构造了一维Tonks-Girardeau原子气区域中Gross-Pitaevskii方程的新解.步骤一,通过函数变换,把一维Tonks-Girardeau原子气区域中Gross-Pitaevskii方程的求解问题转化为一种非线性常微分方程的求解问题.步骤二,给出了一种非线性常微分方程与第二种椭圆方程的拟Bcklund变换.步骤三,利用第二种椭圆方程的新解和Bcklund变换,构造了一维Tonks-Girardeau原子气区域中Gross-Pitaevskii方程的无穷序列新解.The following steps are given to search for new solutions of Gross-Pitaevskii equation in a one-dimensional Tonks-Girardeau atomic gas field. Step one, according to a function transforma- tion, the solving of Gross-Pitaevskii equation in a one-dimensional Tonks-Girardeau atomic gas field is changed into the solving of a kind of nonlinear ordinary differential equations. Step two,a kind of nonlinear ordinary differential equations and the quasi-B^icklund transformation of the second kind of elliptic equations are obtained. Finally, new infinite sequence solutions of Gross-Pitaevskii equa- tion in one-dimensional Tonks-Girardeau atomic gas fields are constructed by applying new solu- tions and Backlund transformation of the second kind of elliptic equations.

关 键 词：函数变换 GROSS-PITAEVSKII方程 BACKLUND变换 无穷序列新解 

分 类 号：O175.29[理学—数学]