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

Xi-Xiang Xu and Meng Xu

Discrete Dynamics in Nature and Society, 2018, vol. 2018, 1-11

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.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:4152917

DOI: 10.1155/2018/4152917

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