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Algebra i Analiz, 2010, Volume 22, Issue 3, Pages 191–205 (Mi aa1192)  

This article is cited in 9 scientific papers (total in 9 papers)

Research Papers

Hirota difference equation and a commutator identity on an associative algebra

A. K. Pogrebkov

Steklov Mathematical Institute, Moscow, Russia
Full-text PDF (626 kB) Citations (9)
References:
Abstract: In earlier papers of the author it was shown that some simple commutator identities on an associative algebra generate integrable nonlinear equations. Here, this observation is generalized to the case of difference nonlinear equations. The identity under study leads, under a special realization of the elements of the associative algebra, to the famous Hirota difference equation. Direct and inverse problems are considered for this equation, as well as some properties of its solutions. Finally, some other commutator identities are discussed and their relationship with integrable nonlinear equations, both differential and difference, is demonstrated.
Keywords: Hirota difference equation, commutator identity, extended operators, direct and inverse problems.
Received: 19.02.2010
English version:
St. Petersburg Mathematical Journal, 2011, Volume 22, Issue 3, Pages 473–483
DOI: https://doi.org/10.1090/S1061-0022-2011-01153-7
Bibliographic databases:
Document Type: Article
Language: English
Citation: A. K. Pogrebkov, “Hirota difference equation and a commutator identity on an associative algebra”, Algebra i Analiz, 22:3 (2010), 191–205; St. Petersburg Math. J., 22:3 (2011), 473–483
Citation in format AMSBIB
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  • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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