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The long wave limiting of the discrete nonlinear evolution equations

Author

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  • Zhang, Yi
  • Zhao, Hai-qiong
  • Li, Ji-bin

Abstract

We show here that rational, positon, negaton, breather solutions of some discrete nonlinear evolution equations are presented via long wave limiting method. The discrete nonlinear evolution equations concerned are 1D Toda lattice, differential-difference KdV, differential-difference analogue KdV equations.

Suggested Citation

  • Zhang, Yi & Zhao, Hai-qiong & Li, Ji-bin, 2009. "The long wave limiting of the discrete nonlinear evolution equations," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2965-2972.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:5:p:2965-2972
    DOI: 10.1016/j.chaos.2009.04.047
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    References listed on IDEAS

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    1. Zhang, Da-jun, 2005. "Singular solutions in Casoratian form for two differential-difference equations," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1333-1350.
    2. 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.
    3. Ma, Wen-Xiu, 2005. "Complexiton solutions of the Korteweg–de Vries equation with self-consistent sources," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1453-1458.
    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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