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The limit solutions of the difference–difference KdV equation

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  • Chen, Peng
  • Wang, Guang-sheng
  • Zhang, Da-jun

Abstract

This paper describes an exact limit procedure by which a simple formula for the N-double-pole solution to the difference–difference KdV equation is derived from its 2N-soliton solution in Hirota’s form. This limit procedure is general and can apply to other soliton equations with multi-soliton solutions in Hirota’s form.

Suggested Citation

  • Chen, Peng & Wang, Guang-sheng & Zhang, Da-jun, 2009. "The limit solutions of the difference–difference KdV equation," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 376-381.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:1:p:376-381
    DOI: 10.1016/j.chaos.2007.07.072
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    References listed on IDEAS

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    1. Sun, Mei-na & Deng, Shu-fang & Chen, Deng-yuan, 2005. "The Bäcklund transformation and novel solutions for the Toda lattice," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1169-1175.
    2. Deng, Shu-fang, 2005. "Bäcklund transformation and soliton solutions for KP equation," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 475-480.
    3. Zhang, Yi & Chen, Deng-yuan, 2005. "A new representation of N-soliton solution and limiting solutions for the fifth order KdV equation," Chaos, Solitons & Fractals, Elsevier, vol. 23(3), pages 1055-1061.
    4. Zhang, Yi & Chen, Deng-yuan & Li, Zhi-bin, 2006. "A direct method for deriving a multisoliton solution to the fifth order KdV equation," Chaos, Solitons & Fractals, Elsevier, vol. 29(5), pages 1188-1193.
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