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

Autor:	Maciej Nieszporski, James Atkinson
Rok vydání:	2013
Předmět:	Algebra Polynomial Quadratic equation Integrable system Discriminant Degree (graph theory) Factorization Simultaneous equations Independent equation General Mathematics Mathematics
Zdroj:	International Mathematics Research Notices. 2014:4215-4240
ISSN:	1687-0247 1073-7928
DOI:	10.1093/imrn/rnt066
Popis:	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 Backlund transformations connecting all but the primary multi-quadratic model back to equations from the multi-affine class.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::c4d1ec7d58bd88928ddb1c5b12da7075 https://doi.org/10.1093/imrn/rnt066 Zobrazit plný text záznamu