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Teoreticheskaya i Matematicheskaya Fizika, 2009, Volume 161, Number 3, Pages 332–345
DOI: https://doi.org/10.4213/tmf6445
(Mi tmf6445)
 

This article is cited in 6 scientific papers (total in 6 papers)

An integrable class of differential equations with nonlocal nonlinearity on Lie groups

M. M. Goncharovskiy, I. V. Shirokov

Omsk State University for Technology, Omsk, Russia
Full-text PDF (729 kB) Citations (6)
References:
Abstract: We construct the general and $N$-soliton solutions of an integro-differential Schrödinger equation with a nonlocal nonlinearity. We consider integrable nonlinear integro-differential equations on the manifold of an arbitrary connected unimodular Lie group. To reduce the equations on the group to equations with a smaller number of independent variables, we use the method of orbits in the coadjoint representation and the generalized harmonic analysis based on it. We demonstrate the capacities of the algorithm with the example of the $SO(3)$ group.
Keywords: nonlinear integro-differential equation, soliton, Lie group, coadjoint representation, harmonic analysis.
Received: 01.03.2009
English version:
Theoretical and Mathematical Physics, 2009, Volume 161, Issue 3, Pages 1604–1615
DOI: https://doi.org/10.1007/s11232-009-0149-5
Bibliographic databases:
Language: Russian
Citation: M. M. Goncharovskiy, I. V. Shirokov, “An integrable class of differential equations with nonlocal nonlinearity on Lie groups”, TMF, 161:3 (2009), 332–345; Theoret. and Math. Phys., 161:3 (2009), 1604–1615
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf6445
  • https://doi.org/10.4213/tmf6445
  • https://www.mathnet.ru/eng/tmf/v161/i3/p332
  • This publication is cited in the following 6 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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    Abstract page:718
    Full-text PDF :236
    References:103
    First page:30
     
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