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Multiquadratic quad equations: integrable cases from a factorised discriminant hypothesis
 Intl. Math. Res. Not
"... Abstract. We give integrable quad equations which are multiquadratic (degreetwo) counterparts of the wellknown multiaffine (degreeone) equations classified by Adler, Bobenko and Suris (ABS). These multiquadratic equations define multivalued evolution from initial data, but our construction is ..."
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Abstract. We give integrable quad equations which are multiquadratic (degreetwo) counterparts of the wellknown multiaffine (degreeone) equations classified by Adler, Bobenko and Suris (ABS). These multiquadratic equations define multivalued evolution from initial data, but our construction is based on the hypothesis that discriminants of the defining polynomial factorise in a particular way that allows to reformulate the equation as a singlevalued system. Such reformulation comes at the cost of introducing auxiliary (edge) variables and augmenting the initial data. Like the multiaffine equations listed by ABS, these new models are consistent in multidimensions. We clarify their relationship with the ABS list by obtaining Bäcklund transformations connecting all but the primary multiquadratic model back to equations from the multiaffine class. 1.
Families of Integrable Equations
 SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS
, 2011
"... We present a method to obtain families of lattice equations. Specifically we focus on two of such families, which include 3parameters and their members are connected through Bäcklund transformations. At least one of the members of each family is integrable, hence the whole family inherits some inte ..."
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We present a method to obtain families of lattice equations. Specifically we focus on two of such families, which include 3parameters and their members are connected through Bäcklund transformations. At least one of the members of each family is integrable, hence the whole family inherits some integrability properties.
Darboux Transformations, Discrete Integrable Systems and Related YangBaxter Maps
, 2014
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