变系数薛定谔方程的Painlevé分析及解析解  

Painlevé analysis and solutions of variable coefficient Schrdinger equation

作　　者：李英杰 智红燕 LI Yingjie;ZHI Hongyan(College of Science, China University of Petroleum （East China） Qingdao 266580, Chin)

机构地区：[1]中国石油大学(华东)理学院

出　　处：《量子电子学报》2017年第6期682-690,共9页Chinese Journal of Quantum Electronics

基　　金：国家自然科学基金;11401584~~

摘　　要：基于简化的Weiss-Tabor-Carnevale(WTC)算法和符号计算,研究了含时空变系数非线性薛定谔方程的Painlevé性质及解析解。方程的4个变系数中前2个是纵向距离的二阶色散和非线性系数,后2个为光纤损耗因子的实部和虚部。利用WTC方法推导了方程具有Painlevé可积性时4个变系数之间的关系。用Painlevé截断法求出了其具有3种特殊形式的有理函数解,用变量分离法求得了该方程的部分解,所得结果是对现有结论的推广。Based on the simplified Weiss-Tabor-Carnevale （WTC） algorithm and symbolic computation, Painleve properties and analytic solutions of the variable coefficient nonlinear SchrSdinger （NLS） equation are investigated, which involves four arbitrary functions of space-time. Among the four variable coefficients of the equation, the first two are two-order dispersion of longitudinal distance and nonlinear coefficient respectively, and the last two are the real and imaginary parts of the fiber loss factor. Relationship among the four variable coefficients are derived with WTC method when the equation is Painlev~ integrable. Three special forms of rational function solutions are derived with Painlev~ truncation method, and the partial solutions of the equation are obtained by using the variable separation method. The obtained results are the extension of existing conclusions.

关 键 词：非线性方程 变系数非线性薛定谔方程 孤子解 有理函数解 WTC算法 

分 类 号：O175.29[理学—数学]