On Decomposition of the ABS Lattice Equations and Related Bäcklund Transformations
- https://doi.org/10.1080/14029251.2018.1440741How to use a DOI?
- ABS list, decomposition, Bäcklund transformation, solutions, weak Lax pair
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.
- © 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 -