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Bäcklund Transformation And Analytic Solutions For A Generalized Variable-Coefficient Modified Korteweg–De Vries Model From Fluid Dynamics And Plasmas

Author

Listed:
  • FU-WEI SUN

    (Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China;
    College of Science, North China University of Technology, Beijing 100144, China)

  • YI-TIAN GAO

    (Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China;
    State Key Laboratory of Software Development Environment, Beijing University of Aeronautics and Astronautics, Beijing 100191, China)

  • CHUN-YI ZHANG

    (Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China;
    Meteorology Center of Air Force Command Post, Changchun 130051, China)

  • XIAO-GE XU

    (Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China;
    Beijing Information Technology Institute, Beijing 100101, China)

Abstract

We investigate a generalized variable-coefficient modified Korteweg–de Vries model with perturbed factor and external force (vc-GmKdV) describing fluid dynamics and space plasmas. In this paper, we propose an extended variable-coefficient balancing-act method (Evc-BAM), which is concise and straightforward, to obtain the generalized analytic solutions including solitary wave solution of the vc-GmKdV model with symbolic computation. Meanwhile, using the Evc-BAM, we obtain an auto-Bäcklund transformation for the vc-GmKdV model on the relevant constraint conditions of the coefficient functions. Using the given auto-Bäcklund transformation, the solutions of special equations for the vc-GmKdV model are also obtained as the variable-coefficient Korteweg–de Vries (vc-KdV) equation, the generalized KdV equation with perturbed factor and external force (GKdV), the variable-coefficient modified Korteweg–de Vries (vc-mKdV) equation, and the variable-coefficient cylindrical modified Korteweg–de Vries (vc-cmKdV) equation, respectively.

Suggested Citation

  • Fu-Wei Sun & Yi-Tian Gao & Chun-Yi Zhang & Xiao-Ge Xu, 2008. "Bäcklund Transformation And Analytic Solutions For A Generalized Variable-Coefficient Modified Korteweg–De Vries Model From Fluid Dynamics And Plasmas," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 19(11), pages 1659-1671.
    • Handle: RePEc:wsi:ijmpcx:v:19:y:2008:i:11:n:s0129183108013199
    DOI: 10.1142/S0129183108013199
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