On decomposition of the ABS lattice equations and related B\"acklund transformations
Exactly Solvable and Integrable Systems
2017-05-03 v1
Abstract
The Adler-Bobenko-Suris (ABS) list contains all scalar quadrilateral equations which are consistent around the cube. Each equation in the ABS list admits a beautiful decomposition. In this paper, we first revisit these decomposition formulas, by which we construct B\"acklund transformations (BTs) and consistent triplets. Some BTs are used to construct new solutions, lattice equations and weak Lax pairs.
Keywords
Cite
@article{arxiv.1705.00843,
title = {On decomposition of the ABS lattice equations and related B\"acklund transformations},
author = {Danda Zhang and Da-jun Zhang},
journal= {arXiv preprint arXiv:1705.00843},
year = {2017}
}
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20 pages