Journal of Nonlinear Mathematical Physics

Volume 25, Issue 1, February 2018, Pages 34 - 53

On Decomposition of the ABS Lattice Equations and Related Bäcklund Transformations

Authors
Danda Zhang, Da-jun Zhang*
Department of Mathematics, Shanghai University, Shanghai, 200444, People’s Republic of China
*Corresponding author. djzhang@staff.shu.edu.cn
Corresponding Author
Da-jun Zhang
Received 10 May 2017, Accepted 7 August 2017, Available Online 6 January 2021.
DOI
https://doi.org/10.1080/14029251.2018.1440741How to use a DOI?
Keywords
ABS list, decomposition, Bäcklund transformation, solutions, weak Lax pair
Abstract

The Adler-Bobenko-Suris (ABS) list contains scalar quadrilateral equations which are consistent around the cube, and have D4 symmetry and tetrahedron property. Each equation in the ABS list admits a beautiful decomposition. We revisit these decomposition formulas and by means of them we construct Bäcklund transformations (BTs). BTs are used to construct lattice equations, their new solutions and weak Lax pairs.

Copyright
© 2018 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
25 - 1
Pages
34 - 53
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1080/14029251.2018.1440741How to use a DOI?
Copyright
© 2018 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Danda Zhang
AU  - Da-jun Zhang
PY  - 2021
DA  - 2021/01
TI  - On Decomposition of the ABS Lattice Equations and Related Bäcklund Transformations
JO  - Journal of Nonlinear Mathematical Physics
SP  - 34
EP  - 53
VL  - 25
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2018.1440741
DO  - https://doi.org/10.1080/14029251.2018.1440741
ID  - Zhang2021
ER  -