非齐次光纤介质中非线性薛定谔方程的相似变换与精确解
PDF下载 (827)张 娜,李 彪*.非齐次光纤介质中非线性薛定谔方程的相似变换与精确解[J].宁波大学学报(理工版),2016,29(3):8-12.DOI:
ZHANG Na,LI Biao*.Similarity Transformation and Exact Solutions to Nonlinear Schr?dinger Equation in Inhomogeneous Optical Fiber Media[J].Journal of Ningbo University(Natural Science & Engineering Edition),2016,29(3):8-12.DOI:
| Title: | Similarity Transformation and Exact Solutions to Nonlinear Schr?dinger Equation in Inhomogeneous Optical Fiber Media |
| 作者: | 张 娜, 李 彪* |
| Author(s): | ZHANG Na, LI Biao* |
| 关键词: | 非线性薛定谔方程; 相似变换; 精确解; 符号计算 |
| Keywords: | nonlinear Schr?dinger equation; similarity transformation; exact solutions; symbolic computation |
| 分类号: | O175.29 |
| 文献标识码: | A |
| 摘要: | 基于李群理论和符号计算, 获得了具有增益/损耗项和频率啁啾项的非齐次光纤介质中的非线性薛定谔方程的相似变换; 利用所得变换, 把具有群速度参数、克尔非线性效应参数、相位调制参数和增益/损耗参数的变系数非线性薛定谔方程约化为相应常系数非线性薛定谔方程. 通过一个广义的直接求解方法, 构造了常系数非线性薛定谔方程的一组亮孤子解和一组暗孤子解, 进而得到了变系数非线性薛定谔方程丰富的精确解. 最后对所得亮孤子解和暗孤子解进行了动力学分析与讨论. |
| Abstract: | On the basis of Lie group theory and symbolic computation, a similarity transformation is constructed for the nonlinear Schr?dinger (NLS) equation in the inhomogeneous optical fiber media. The related constant-coefficients NLS equations are derived from the inhomogeneous NLS equation with the group velocity dispersion parameter, the Kerr nonlinearity and the inhomogeneous parameters related to phase modulation and loss/gain. Using a generalized direct assumption method, a family of bright soliton solutions and a family of dark soliton solutions are obtained from its related constant-coefficient NLS equation. Finally, nonlinear dynamics of the obtained solutions is discussed and analyzed. |
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| 备注/Memo: | 收稿日期: 2015?12?21. 宁波大学学报（理工版）网址: http://journallg.nbu.edu.cn/ 基金项目: 国家自然科学基金（11271211）. 第一作者: 张娜（1989－）, 女, 河南遂平人, 在读硕士研究生, 主要研究方向: 孤子理论与应用. E-mail: 1243880917@qq.com *通信作者: 李彪（1971－）, 男, 湖南会同人, 教授, 主要研究方向: 数学物理与数学机械化. E-mail: libiao@nbu.edu.cn 宁波大学学报（理工版）网址：http://journallg.nbu.edu.cn/ |
