Multi-Quadratic Quad Equations: Integrable Cases from a Factorized-Discriminant Hypothesis

Atkinson, James and Nieszporski, Maciej (2013) Multi-Quadratic Quad Equations: Integrable Cases from a Factorized-Discriminant Hypothesis. International Mathematics Research Notices, n/a (n/a). n/a-n/a. ISSN 1073-7928

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Official URL: http://dx.doi.org/10.1093/imrn/rnt066

Abstract

We give integrable quad equations that are multi-quadratic (degree 2) counterparts of the well-known multi-affine (degree 1) equations classified by Adler, Bobenko, and Suris (ABS). These multi-quadratic equations define multi-valued evolution from initial data, but our construction is based on the hypothesis that discriminants of the defining polynomial factorize in a particular way that allows to reformulate the equation as a single-valued system. Such reformulation comes at the cost of introducing auxiliary (edge) variables and augmenting the initial data. Like the multi-affine equations listed by ABS, these new models are consistent in multi-dimensions. We clarify their relationship with the ABS list by obtaining Bäcklund transformations connecting all but the primary multi-quadratic model back to equations from the multi-affine class.

Item Type: Article
Additional Information: Published online before print.
Subjects: G100 Mathematics
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: Becky Skoyles
Date Deposited: 02 Oct 2013 10:01
Last Modified: 10 Aug 2015 11:10
URI: http://nrl.northumbria.ac.uk/id/eprint/13629

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