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柱(球)非线性薛定谔方程的精确解 被引量：4

Exact Solutions of Cylindrically(Spherically) Nonlinear Schrdinger Equation
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摘要 研究了柱(球)非线性薛定谔方程(CS-NLS),导出了一个CS-NLS与变系数非线性薛定谔方程(NLS)之间的相似变换,变系数NLS的解可用G'/G-展开法获得。根据该相似变换,分别利用变系数NLS以及常系数NLS的解,得到了CS-NLS的精确解。特别地,还得到了色散系数和非线性系数均为常数的CS-NLS的精确解。 The cylindrically( spherically) nonlinear Schrdinger equation( CS-NLS) was studied. A similarity transformation between the CS-NLS and NLS with variable coefficients was obtained. The solutions of the NLS with variable coefficients were obtained by using G'/G-expansion method. According to the similarity transformation,by using the solutions of NLS with variable coefficients and solutions of NLS with constant coefficients,the exact solutions of the CS-NLS were obtained.Specially the exact solutions of the CS-NLS withconstant disperson coefficient and nonlinear coefficient are obtained.
作者 李景美 张金良 王飞
机构地区 河南科技大学数学与统计学院
出处 《河南科技大学学报（自然科学版）》 CAS 北大核心 2018年第2期83-86,共4页 Journal of Henan University of Science And Technology:Natural Science
基金 国家自然科学基金项目(51675161) 河南科技大学大学生研究训练计划(SRTP)基金项目(2017159)
关键词 柱(球)非线性薛定谔方程 变系数非线性薛定谔方程 相似变换 G'/G-展开法 精确解 cylindrically(spherically) nonlinear Schrdinger equation nonlinear Schrdinger equation with variable coefficients similarity transformation G'/G-expansion method exact solution
分类号 O175.2 [理学—基础数学]
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河南科技大学学报（自然科学版）
2018年 第2期

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