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

This article is cited in 5 scientific papers (total in 5 papers)

Research Papers

Hirota difference equation and a commutator identity on an associative algebra

A. K. Pogrebkov

Steklov Mathematical Institute, Moscow, Russia

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.

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English version:
St. Petersburg Mathematical Journal, 2011, 22:3, 473–483

Bibliographic databases:

Document Type: Article
Received: 19.02.2010
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

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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. A. K. Pogrebkov, “Hirota difference equation: Inverse scattering transform, Darboux transformation, and solitons”, Theoret. and Math. Phys., 181:3 (2014), 1585–1598  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. A. K. Pogrebkov, “Commutator identities on associative algebras, the non-Abelian Hirota difference equation and its reductions”, Theoret. and Math. Phys., 187:3 (2016), 823–834  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    3. Andrei K. Pogrebkov, “Symmetries of the Hirota Difference Equation”, SIGMA, 13 (2017), 053, 14 pp.  mathnet  crossref  mathscinet
    4. A. K. Pogrebkov, “Higher Hirota difference equations and their reductions”, Theoret. and Math. Phys., 197:3 (2018), 1779–1796  mathnet  crossref  crossref  adsnasa  isi  elib
    5. Pogrebkov A., “Hirota Difference Equation and Darboux System: Mutual Symmetry”, Symmetry-Basel, 11:3 (2019), 436  crossref  isi
  • Алгебра и анализ St. Petersburg Mathematical Journal
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