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A simple method for generating integrable hierarchies with multi-potential functions

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  • Fan, Engui
  • Zhang, Yufeng

Abstract

A simple efficient method for obtaining integrable hierarchies of evolution equations with multi-potential functions is proposed. By making use of the concept of cycled numbers, a new loop algebra A∼1∗ is constructed. Taking account of applicable convenience, a few subalgebras of the loop algebra A∼1∗ are presented again, from one of them, two new integrable Hamiltonian hierarchies with multi-potential functions are obtained. Finally, a 3×3 loop algebra G∼ with five dimensions is established, from which a coupled integrable coupling system of one of the above integrable hierarchies is derived. The approach presented in this paper can be used generally.

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  • Fan, Engui & Zhang, Yufeng, 2005. "A simple method for generating integrable hierarchies with multi-potential functions," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 425-439.
    • Handle: RePEc:eee:chsofr:v:25:y:2005:i:2:p:425-439
    DOI: 10.1016/j.chaos.2004.08.010
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    Cited by:

    1. Yan, Wang & Zhang, Yufeng, 2008. "Expansion of the Lie algebras and integrable couplings," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 541-547.
    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.

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