|Title:||Discriminantly separable polynomials and quad-equations||Journal:||Journal of Geometric Mechanics||Volume:||6||Issue:||3||First page:||319||Last page:||333||Issue Date:||1-Jan-2014||Rank:||M21||ISSN:||1941-4889||DOI:||10.3934/jgm.2014.6.319||Abstract:||
We classify the discriminantly separable polynomials of degree two in each of three variables, defined by a property that all the discriminants as polynomials of two variables are factorized as products of two polynomials of one variable each. Our classification is based on the study of structures of zeros of a polynomial component P of a discriminant. This classification is related to the classification of pencils of conics in a delicate way. We establish a relationship between our classification and the classification of integrable quad-equations which has been suggested recently by Adler, Bobenko, and Suris.
|Keywords:||Discriminantly separable polynomials | Integrable quad-equations | Möbius transformations | Pencils of conics | Two-valued groups||Publisher:||American Institute of Mathematical Sciences|
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