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高校应用数学学报
高校应用数学学报  2016, Vol. 31 Issue (2): 176-184    
    
一类广义非线性Schrodinger扰动方程的泛函渐近解法
欧阳成1, 汪维刚2, 石兰芳3, 莫嘉琪4
1. 湖州师范学院 理学院, 浙江湖州 313000
2. 桐城师范高等专科学校 理工系, 安徽桐城 231402
3. 南京信息工程大学 数学与统计学院, 江苏南京 210044
4. 安徽师范大学 数学系, 安徽芜湖 241003
A class of functional asymptotic method for the generalized nonlinear disturbed Schrodinger equation
OUYANG Cheng1, WANG Wei-gang2, SHI Lang-fang3, MO Jia-qi4
1. Faculty of Science, Huzhou University, Huzhou 313000, China
2. Tongcheng Teaching Department , Anqing Teacher’s College, Tongcheng 231400, China
3. College of Mathematics and Statistics, Nanjing University of Information Science & Technology, Nanjing 210044, China
4. Department of Mathematics, Anhui Normal University, Wuhu 241003, China
 全文: PDF 
摘要： 研究了一类非线性Schrodinger扰动耦合系统. 利用近似解相关联的特殊方法,首先讨论了对应的线性系统, 并得到了其精确解. 再利用泛函迭代的方法得到了非线性Schrodinger扰动耦合系统的泛函渐近解析解. 这个渐近解是一个解析式, 还可对它进行解析运算. 这对使用简单的模拟方法得到的近似解是达不到的.
关键词： 非线性方程;  耦合系统;  近似解    
Abstract: A class of the generalized disturbed nonlinear Schr¨odinger coupled system is studied. Using the specific technique relates to the approximate solutions, the corresponding linear system is first considered and its exact solution is obtained. Then, the functional asymptotic analytic solution of the nonlinear Schr¨odinger disturbed coupled model is found by using a valid method. The obtained asymptotic solution is an analytic expression, so it could also carry on analytic operations. These cannot happen to the simple simulate method.
Key words: nonlinear equation    coupled system    approximate solution
收稿日期: 2015-02-12 出版日期: 2018-05-17
CLC:  O175.29  
基金资助: 国家自然科学基金(11202106); 浙江省自然科学基金(LY13A010005); 江苏省自然科学基金(13KJB170016)
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欧阳成
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引用本文:

欧阳成, 汪维刚, 石兰芳, 莫嘉琪. 一类广义非线性Schrodinger扰动方程的泛函渐近解法[J]. 高校应用数学学报, 2016, 31(2): 176-184.

OUYANG Cheng, WANG Wei-gang, SHI Lang-fang, MO Jia-qi. A class of functional asymptotic method for the generalized nonlinear disturbed Schrodinger equation. Applied Mathematics A Journal of Chinese Universities, 2016, 31(2): 176-184.

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http://www.zjujournals.com/amjcua/CN/    或    http://www.zjujournals.com/amjcua/CN/Y2016/V31/I2/176

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