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A new Lie algebra and soliton solutions, Bächlund transformation of soliton equations

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  • Tam, Hon-Wah
  • Zhang, Yufeng

Abstract

A new Lie algebra is introduced for which a soliton hierarchy of nonlinear evolution equations is derived from zero curvature equations. A reduced equation from the hierarchy is obtained whose exact solutions are produced. Again using the Lie algebra and the corresponding loop algebra, a type of nonlinear soliton equations with exponential terms in potential functions are given. The Bäcklund transformation among them is also generated.

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  • Tam, Hon-Wah & Zhang, Yufeng, 2009. "A new Lie algebra and soliton solutions, Bächlund transformation of soliton equations," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1670-1676.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:3:p:1670-1676
    DOI: 10.1016/j.chaos.2009.03.062
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    References listed on IDEAS

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    1. Zhang, Yufeng & Tam, Honwah, 2007. "A few subalgebras of the Lie algebra A3 and a direct approach for obtaining integrable couplings," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1424-1432.
    2. Fan, Engui & Zhang, Yufeng, 2006. "Vector loop algebra and its applications to integrable system," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 966-971.
    3. Zhang, Yufeng & Guo, Xiurong & Tam, Honwah, 2006. "A new Lie algebra, a corresponding multi-component integrable hierarchy and an integrable coupling," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 114-124.
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