A family of integrable different-difference equations, its Hamiltonian structure, and Darboux-Bäcklund transformation
type: Item
instance of: scholarly article
title: A family of integrable different-difference equations, its Hamiltonian structure, and Darboux-Bäcklund transformation
zbMATH Open document ID: 1417.39062
DOI: 10.1155/2018/4152917
author: Xi-Xiang Xu
author: Meng Xu
published in: Discrete Dynamics in Nature and Society
publication date: 2019-02-20T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 39A30
zbMATH DE Number: 7026574
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/4152917
OpenAlex ID: W2807228324
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description: scientific article; zbMATH DE number 7026574