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Teoreticheskaya i Matematicheskaya Fizika, 2009, Volume 159, Number 3, Pages 502–514
DOI: https://doi.org/10.4213/tmf6368 (Mi tmf6368) 		 
This article is cited in 3 scientific papers (total in 3 papers)

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

B. G. Konopelchenko

Università del Salento
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DOI: https://doi.org/10.4213/tmf6368
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.
English version:
Theoretical and Mathematical Physics, 2009, Volume 159, Issue 3, Pages 842–852
DOI: https://doi.org/10.1007/s11232-009-0072-9
Bibliographic databases:
Language: Russian
Citation: B. G. Konopelchenko, “Continuous-discrete integrable equations and Darboux transformations as deformations of associative algebras”, TMF, 159:3 (2009), 502–514; Theoret. and Math. Phys., 159:3 (2009), 842–852
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf/v159/i3/p502
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
     
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