Continuous-discrete integrable equations and Darboux transformations as deformations of associative algebras

Details Continuous-discrete integrable equations and Darboux transformations as deformations of associative algebras Continuous-discrete integrable equations and Darboux transformations as deformations of associative algebras

2008-09-23

arxiv.org/abs/0809.3852v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Scientific paper

Deformations of the structure constants for a class of associative noncommutative algebras generated by Deformation Driving Algebras (DDA's) are defined and studied. These deformations are governed by the Central System (CS). Such a CS is studied for the case of DDA being the algebra of shifts. Concrete examples of deformations for the three-dimensional algebra governed by discrete and mixed continuous-discrete Boussinesq (BSQ) and WDVV equations are presented. It is shown that the theory of the Darboux transformations, at least for the BSQ case, is completely incorporated into the proposed scheme of deformations.

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