This article is cited in 3 papers

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

B. G. Konopelchenko

Università del Salento

Abstract: We define and study deformations of the structure constants for a certain class of associative noncommutative algebras generated by deformation-driving algebras (DDAs). These deformations are governed by the central system (CS). We study such a CS in the case where the DDA is the algebra of shifts. We present concrete examples of deformations for the three-dimensional algebra governed by discrete and mixed continuous-discrete Boussinesq (BSQ) and WDVV equations. We show that the theory of Darboux transformations is completely incorporated into the proposed scheme of deformations, at least in the BSQ case.

Keywords: associative algebra, deformation, integrable system.

DOI: 10.4213/tmf6368

 English version: Theoretical and Mathematical Physics, 2009, 159:3, 842–852

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