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Soliton-like solutions and periodic form solutions for two variable-coefficient evolution equations using symbolic computation

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Summary.

Some variable-coefficient generalizations of some nonlinear evolution equations (NLEEs) bear more realistic physical importance. By means of a generalized Riccati equation expansion (GREE) method and a symbolic computation system – Maple – we investigate the variable-coefficient Fisher-type equation and the nearly concentric KdV equation. As a result, rich families of exact analytic solutions for these two equations, including the non-travelling wave’s and coefficient functions’ soliton-like solutions, singular soliton-like solutions, and periodic form solutions, are obtained.

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Acknowledgments.

We would like to express our sincere thanks to Prof. Dr. H. Troger and the referee for their valuable comments and kind help. The work is supported by the National Natural Science Foundation of China under the Grant No. 10072013.

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Authors and Affiliations

  1. Department of Applied Mathematics, Dalian University of Technology, Dalian, 116024, China

    B. Li

  2. Department of Mathematics, Ningbo University, Ningbo, 315211, China

    Y. Chen

  3. Department of Physics, Shanghai Jiao-Tong University, Shanghai, 200030, China

    H. Q. Zhang

  4. Key Laboratory of Mathematics Mechanization, Chinese Academy of Sciences, Beijing, 10080, China

    B. Li, Y. Chen & H. Q. Zhang

Authors
  1. B. Li
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  2. Y. Chen
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  3. H. Q. Zhang
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Correspondence to B. Li.

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Li, B., Chen, Y. & Zhang, H. Soliton-like solutions and periodic form solutions for two variable-coefficient evolution equations using symbolic computation. Acta Mechanica 174, 77–89 (2005). https://doi.org/10.1007/s00707-004-0156-4

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  • DOI: https://doi.org/10.1007/s00707-004-0156-4

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