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

James Atkinson, Maciej Nieszporski

    Research output: Contribution to journalArticlepeer-review

    17 Citations (Scopus)

    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.
    Original languageEnglish
    Pages (from-to)n/a-n/a
    JournalInternational Mathematics Research Notices
    Volumen/a
    Issue numbern/a
    DOIs
    Publication statusPublished - 2013

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