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TMF, 2009, Volume 159, Number 3, Pages 502–514 (Mi tmf6368)  

This article is cited in 2 scientific papers (total in 2 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: https://doi.org/10.4213/tmf6368

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

Bibliographic databases:


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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  • http://mi.mathnet.ru/eng/tmf6368
  • https://doi.org/10.4213/tmf6368
  • http://mi.mathnet.ru/eng/tmf/v159/i3/p502

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Konopelchenko, BG, “Discrete integrable systems and deformations of associative algebras”, Journal of Physics A-Mathematical and Theoretical, 42:45 (2009), 454003  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    2. Pavlov M.V., Sergyeyev A., “Oriented Associativity Equations and Symmetry Consistent Conjugate Curvilinear Coordinate Nets”, J. Geom. Phys., 85 (2014), 46–59  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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