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

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Abstract

The Painlevé 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 Painlevé 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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Authors and Affiliations

  1. Department of Electronic Engineering, University of Electronic Science and Technology of China Zhongshan Institute, Zhongshan 5, 28402, Guangdong Province, P. R. China

    ** Liu  (刘 萍)

  2. Department of Marine Meteorology, Ocean University of China, Qingdao, 266100, Shandong Province, P. R. China

    Zi-liang Li  (**子良)

  3. Department of Physics, Shanghai Jiao Tong University, Shanghai, 200240, P. R. China

    Sen-yue Lou  (楼森岳)

  4. Faculty of Science, Ningbo University, Ningbo, 315211, Zhejiang Province, P. R. China

    Sen-yue Lou  (楼森岳)

Authors
  1. ** Liu  (刘 萍)
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  2. Zi-liang Li  (**子良)
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  3. Sen-yue Lou  (楼森岳)
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Corresponding author

Correspondence to ** Liu  (刘 萍).

Additional information

Communicated by Zhe-wei ZHOU

Project supported by the National Natural Science Foundation of China (Nos. 10735030 and 40775069), the Natural Science Foundation of Guangdong Province of China (No. 10452840301004616), and the Scientific Research Foundation for the Doctors of University of Electronic Science and Technology of China Zhongshan Institute (No. 408YKQ09)

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Liu, P., Li, Zl. & Lou, Sy. A class of coupled nonlinear Schrödinger equations: Painlevé property, exact solutions, and application to atmospheric gravity waves. Appl. Math. Mech.-Engl. Ed. 31, 1383–1404 (2010). https://doi.org/10.1007/s10483-010-1370-6

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  • DOI: https://doi.org/10.1007/s10483-010-1370-6

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