一类耦合非线性Schrodinger方程的Painlevé性质、严格解及其在大气重力波中的应用

刘萍; 李子良; 楼森岳

doi:10.3879/j.issn.1000-0887.2010.11.005

一类耦合非线性Schrodinger方程的Painlevé性质、严格解及其在大气重力波中的应用

doi: 10.3879/j.issn.1000-0887.2010.11.005

电子科技大学中山学院电子工程系,广东中山 528402;2.中国海洋大学海洋气象系,山东青岛 266100;3.上海交通大学物理系,上海 200240; 4.宁波大学理学院,浙江宁波 315211

基金项目: 广东省自然科学基金资助项目(10452840301004616);国家自然科学基金资助项目(10735030;40775069);电子科技大学中山学院博士启动基金项目(408YKQ09)资助

详细信息

作者简介:
刘萍(1980- ),女,湖北人,博士(联系人.E-mail:liuping49@126.com).

中图分类号: P431
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出版历程
- 收稿日期: 1900-01-01
- 修回日期: 2010-09-30
- 刊出日期: 2010-11-15

A Class of Coupled Nonlinear Schrödinger Equation:Painlevé Property,Exact Solutions and Application to Atmospheric Gravity Waves

Department of Electronic Engineering, University of Electronic Science and Technology of China Zhongshan Institute, Zhongshan, Guangdong 528402, P. R. China;

摘要

摘要: 讨论了大气科学里的一类耦合非线性Schrdinger方程的Painlevé可积性和严格解．并给出了这个耦合方程通过Painlevé性质检测的参数条件．应用椭圆余弦函数展开法，得到了这个耦合非线性Schrdinger方程的20个周期椭圆余弦波解．这些严格解被用应用于解释大气重力波的产生和传输机制．
- 耦合非线性Schrdinger方程 /
- Painlevé 性质 /
- 严格解 /
- 大气重力波
Abstract: The Painlev? integrability and exact solutions of a coupled nonlinear Schrödinger (CNLS) equation applied in atmospheric dynamics were discussed. Some parametric restrictions of the CNLS equation were given to pass the Painlevé test. 20 periodic cnoidal wave solutions were obtained by applying the rational expansions of fundamental Jacobi elliptic functions. The exact solutions of the CNLS equation are applied to explain the generation and propagation of atmospheric gravity waves.
- coupled nonlinear Schrö /
- dinger equation /
- Painlevé /
- property

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