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New hierarchies of integrable positive and negative lattice models and Darboux transformation

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  • Yang, Hongxiang
  • Xu, Xixiang
  • Ding, Haiyong

Abstract

Two hierarchies of integrable positive and negative lattice equations associated with a new discrete isospectral problem are derived. It is shown that they correspond to positive and negative power expansions of Lax operators with respect to the spectral parameter, respectively. It is also shown that each equation in the resulting hierarchies is Liouville integrable. As the typical example, a fairly new and infrequent rational equation with regard to potentials is presented. Furthermore, a Darboux transformation is established with the help of gauge transformations of Lax pairs for the typical lattice soliton equations, by means of which the exact solutions are given.

Suggested Citation

  • Yang, Hongxiang & Xu, Xixiang & Ding, Haiyong, 2005. "New hierarchies of integrable positive and negative lattice models and Darboux transformation," Chaos, Solitons & Fractals, Elsevier, vol. 26(4), pages 1091-1103.
    • Handle: RePEc:eee:chsofr:v:26:y:2005:i:4:p:1091-1103
    DOI: 10.1016/j.chaos.2005.02.011
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    Cited by:

    1. Ding, Haiyong & Hua, Peng & Zhang, Junben & Chen, Hongye, 2009. "A discrete iso-spectral problem with positive and negative hierarchies and integrable coupling system," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1497-1503.
    2. Xu, Xi-Xiang, 2015. "A deformed reduced semi-discrete Kaup–Newell equation, the related integrable family and Darboux transformation," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 275-283.
    3. Li, Zhu & Zhang, Ning & Dong, Huanhe, 2009. "New integrable lattice hierarchies and associated properties," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1132-1143.

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