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Exact solitary wave solutions of nonlinear wave equations

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Abstract

The hyperbolic function method for nonlinear wave equations is presented. In support of a computer algebra system, many exact solitary wave solutions of a class of nonlinear wave equations are obtained via the method. The method is based on the fact that the solitary wave solutions are essentially of a localized nature. Writing the solitary wave solutions of a nonlinear wave equation as the polynomials of hyperbolic functions, the nonlinear wave equation can be changed into a nonlinear system of algebraic equations. The system can be solved via Wu Elimination or Gröbner base method. The exact solitary wave solutions of the nonlinear wave equation are obtained including many new exact solitary wave solutions.

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Authors and Affiliations

  1. Institute of Theoretical Physics, Lanzhou University, 730000, Lanzhou, China

    Guixu Zhang & Yishi Duan

  2. Department of Computer Sciences, Lanzhou University, 730000, Lanzhou, China

    Guixu Zhang

  3. Department of Computer Sciences, East China Normal University, 200062, Shanghai, China

    Zhibin Li

Authors
  1. Guixu Zhang
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  2. Zhibin Li
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  3. Yishi Duan
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Correspondence to Yishi Duan.

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Zhang, G., Li, Z. & Duan, Y. Exact solitary wave solutions of nonlinear wave equations. Sci. China Ser. A-Math. 44, 396–401 (2001). https://doi.org/10.1007/BF02878721

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  • DOI: https://doi.org/10.1007/BF02878721

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