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Complexiton solutions of the Korteweg–de Vries equation with self-consistent sources

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  • Ma, Wen-Xiu

Abstract

Complexiton solutions to the Korteweg–de Vires equation with self-consistent sources are presented. The basic technique adopted is the Darboux transformation. The resulting solutions provide evidence that soliton equations with self-consistent sources can have complexiton solutions, in addition to soliton, positon and negaton solutions. This also implies that soliton equations with self-consistent sources possess some kind of analytical characteristics that linear differential equations possess and brings ideas toward classification of exact explicit solutions of nonlinear integrable differential equations.

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  • 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.
    • Handle: RePEc:eee:chsofr:v:26:y:2005:i:5:p:1453-1458
    DOI: 10.1016/j.chaos.2005.03.030
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    References listed on IDEAS

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    1. Ma, Wen-Xiu & Maruno, Ken-ichi, 2004. "Complexiton solutions of the Toda lattice equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 219-237.
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    Cited by:

    1. Wang, Hong-Yan, 2009. "Commutativity of source generation procedure and Bäcklund transformation: A BKP equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(4), pages 779-785.
    2. Zhang, Yi & Sun, YanBo & Xiang, Wen, 2015. "The rogue waves of the KP equation with self-consistent sources," Applied Mathematics and Computation, Elsevier, vol. 263(C), pages 204-213.
    3. Yu, Guo-Fu & Hu, Xing-Biao, 2009. "Extended Gram-type determinant solutions to the Kadomtsev–Petviashvili equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(1), pages 184-191.
    4. 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.

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