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arXiv · 1705.00843

On decomposition of the ABS lattice equations and related B\"acklund transformations

Danda Zhang·Da-jun Zhang
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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.

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Danda Zhang, Da-jun Zhang. 2017-05-02. On decomposition of the ABS lattice equations and related B\"acklund transformations. https://arxiv.org/abs/1705.00843

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