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Applied Mathematics and Mechanics (English Edition) ›› 2010, Vol. 31 ›› Issue (11): 1383-1404.doi: https://doi.org/10.1007/s10483-010-1370-6

• Articles • 上一篇    下一篇

A class of coupled nonlinear Schrödinger equations: Painlev´e property, exact solutions, and application to atmospheric gravity waves

刘萍1 李子良2 楼森岳3,4   

  1. 1. Department of Electronic Engineering, University of Electronic Science and Technology of China Zhongshan Institute, Zhongshan 528402, Guangdong Province, P. R. China;
    2. Department of Marine Meteorology, Ocean University of China, Qingdao 266100, Shandong Province, P. R. China;
    3. Department of Physics, Shanghai Jiao Tong University, Shanghai 200240, P. R. China; 4. Faculty of Science, Ningbo University, Ningbo 315211, Zhejiang Province, P. R. China
  • 收稿日期:2010-04-04 修回日期:2010-09-30 出版日期:2010-11-01 发布日期:2010-11-01

A class of coupled nonlinear Schrödinger equations: Painlev´e property, exact solutions, and application to atmospheric gravity waves

LIU Ping1, LI Zi-Liang2, LOU Sen-Yue3,4   

  1. 1. Department of Electronic Engineering, University of Electronic Science and Technology of China Zhongshan Institute, Zhongshan 528402, Guangdong Province, P. R. China;
    2. Department of Marine Meteorology, Ocean University of China, Qingdao 266100, Shandong Province, P. R. China;
    3. Department of Physics, Shanghai Jiao Tong University, Shanghai 200240, P. R. China; 4. Faculty of Science, Ningbo University, Ningbo 315211, Zhejiang Province, P. R. China
  • Received:2010-04-04 Revised:2010-09-30 Online:2010-11-01 Published:2010-11-01

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摘要： The Painlev´e integrability and exact solutions to a coupled nonlinear Schrödinger (CNLS) equation applied in atmospheric dynamics are discussed. Some parametric restrictions of the CNLS equation are given to pass the Painlev´e test. Twenty periodic cnoidal wave solutions are obtained by applying the rational expansions of fundamental Jacobi elliptic functions. The exact solutions to the CNLS equation are used to explain the generation and propagation of atmospheric gravity waves.

Abstract: The Painlev´e integrability and exact solutions to a coupled nonlinear Schrödinger (CNLS) equation applied in atmospheric dynamics are discussed. Some parametric restrictions of the CNLS equation are given to pass the Painlev´e test. Twenty periodic cnoidal wave solutions are obtained by applying the rational expansions of fundamental Jacobi elliptic functions. The exact solutions to the CNLS equation are used to explain the generation and propagation of atmospheric gravity waves.

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