Discriminantly separable polynomials and quad-equations
Vladimir Il'ich Dragovic, Katarina Kukić · The Journal of Geometric Mechanics · 2014
We classify the discriminantly separable polynomials of degree twoin each of three variables, defined by a property that all thediscriminants as polynomials of two variables are factorized asproducts of two polynomials of one variable each. Ourclassification is based on the study of structures of zeros of apolynomial component $P$ of a discriminant. This classification isrelated to the classification of pencils of conics in a delicateway. We establish a relationship between our classification and theclassification of integrable quad-equations which has been suggestedrecently by Adler, Bobenko, and Suris.