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A Family of Integrable Different-Difference Equations, Its Hamiltonian Structure, and Darboux-Bäcklund Transformation

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  • Xi-Xiang Xu
  • Meng Xu

Abstract

An integrable family of the different-difference equations is derived from a discrete matrix spectral problem by the discrete zero curvature representation. Hamiltonian structure of obtained integrable family is established. Liouville integrability for the obtained family of discrete Hamiltonian systems is proved. Based on the gauge transformation between the Lax pair, a Darboux-Bäcklund transformation of the first nonlinear different-difference equation in obtained family is deduced. Using this Darboux-Bäcklund transformation, an exact solution is presented.

Suggested Citation

  • Xi-Xiang Xu & Meng Xu, 2018. "A Family of Integrable Different-Difference Equations, Its Hamiltonian Structure, and Darboux-Bäcklund Transformation," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-11, June.
    • Handle: RePEc:hin:jnddns:4152917
    DOI: 10.1155/2018/4152917
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    Cited by:

    1. Lu, Rong-Wu & Xu, Xi-Xiang & Zhang, Ning, 2019. "Construction of solutions for an integrable differential-difference equation by Darboux–Bäcklund transformation," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 389-397.

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