On decomposition of the ABS lattice equations and related Bäcklund transformations

2017/05/02 by Danda Zhang, Da‐jun Zhang, Zhang, Danda +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1705.00843

openalex publication_date 2017/05/02 · openalex created_date 2017/05/12 · openalex updated_date 2026/07/28

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 Bäcklund transformations (BTs) and consistent triplets. Some BTs are used to construct new solutions, lattice equations and weak Lax pairs.

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