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Painlevé analysis, auto-Bäcklund transformation and new analytic solutions for a generalized variable-coefficient Korteweg-de Vries (KdV) equation

Author

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  • Guang-Mei Wei
  • Yi-Tian Gao
  • Wei Hu
  • Chun-Yi Zhang

Abstract

There has been considerable interest in the study on the variable-coefficient nonlinear evolution equations in recent years, since they can describe the real situations in many fields of physical and engineering sciences. In this paper, a generalized variable-coefficient KdV (GvcKdV) equation with the external-force and perturbed/dissipative terms is investigated, which can describe the various real situations, including large-amplitude internal waves, blood vessels, Bose-Einstein condensates, rods and positons. The Painlevé analysis leads to the explicit constraint on the variable coefficients for such a equation to pass the Painlevé test. An auto-Bäcklund transformation is provided by use of the truncated Painlevé expansion and symbolic computation. Via the given auto-Bäcklund transformation, three families of analytic solutions are obtained, including the solitonic and periodic solutions. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006

Suggested Citation

  • Guang-Mei Wei & Yi-Tian Gao & Wei Hu & Chun-Yi Zhang, 2006. "Painlevé analysis, auto-Bäcklund transformation and new analytic solutions for a generalized variable-coefficient Korteweg-de Vries (KdV) equation," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 53(3), pages 343-350, October.
    • Handle: RePEc:spr:eurphb:v:53:y:2006:i:3:p:343-350
    DOI: 10.1140/epjb/e2006-00378-3
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    Cited by:

    1. Tianwei Qiu & Zhen Wang & Xiangyu Yang & Guangmei Wei & Fangsen Cui, 2024. "Solitons, Lumps, Breathers, and Interaction Phenomena for a (2+1)-Dimensional Variable-Coefficient Extended Shallow-Water Wave Equation," Mathematics, MDPI, vol. 12(19), pages 1-15, September.

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