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Teoreticheskaya i Matematicheskaya Fizika, 2008, Volume 154, Number 3, Pages 477–491
DOI: https://doi.org/10.4213/tmf6182 (Mi tmf6182) 		 
This article is cited in 15 scientific papers (total in 15 papers)

Commutator identities on associative algebras and the integrability of nonlinear evolution equations

A. K. Pogrebkov

Steklov Mathematical Institute, Russian Academy of Sciences
Full-text PDF (482 kB) Citations (15)
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DOI: https://doi.org/10.4213/tmf6182
Abstract: We show that commutator identities on associative algebras generate solutions of the linearized versions of integrable equations. In addition, we introduce a special dressing procedure in a class of integral operators that allows deriving both the nonlinear integrable equation itself and its Lax pair from such a commutator identity. The problem of constructing new integrable nonlinear evolution equations thus reduces to the problem of constructing commutator identities on associative algebras.
Keywords: nonlinear evolution equation, Lax pair.
English version:
Theoretical and Mathematical Physics, 2008, Volume 154, Issue 3, Pages 405–417
DOI: https://doi.org/10.1007/s11232-008-0035-6
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. K. Pogrebkov, “Commutator identities on associative algebras and the integrability of nonlinear evolution equations”, TMF, 154:3 (2008), 477–491; Theoret. and Math. Phys., 154:3 (2008), 405–417
Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf6182
  • https://www.mathnet.ru/eng/tmf/v154/i3/p477
    • This publication is cited in the following 15 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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