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Teoreticheskaya i Matematicheskaya Fizika, 2001, Volume 127, Number 2, Pages 284–303
DOI: https://doi.org/10.4213/tmf458 (Mi tmf458) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Coulomb Gas Representation for Rational Solutions of the Painlevé Equations

V. G. Marikhin

L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
Full-text PDF (268 kB) Citations (4)
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DOI: https://doi.org/10.4213/tmf458
Abstract: We consider rational solutions for a number of dynamic systems of the type of the nonlinear Schrödinger equation, in particular, the Levi system. We derive the equations for the dynamics of poles and Bäcklund transformations for these solutions. We show that these solutions can be reduced to rational solutions of the Painlevé IV equation, with the equations for the pole dynamics becoming the stationary equations for the two-dimensional Coulomb gas in a parabolic potential. The corresponding Coulomb systems are derived for the Painlevé II-VI equations. Using the Hamiltonian formalism, we construct the spin representation of the Painlevé equations.
Received: 02.11.2000
Revised: 04.01.2001
English version:
Theoretical and Mathematical Physics, 2001, Volume 127, Issue 2, Pages 646–663
DOI: https://doi.org/10.1023/A:1010449603754
Bibliographic databases:
Language: Russian
Citation: V. G. Marikhin, “Coulomb Gas Representation for Rational Solutions of the Painlevé Equations”, TMF, 127:2 (2001), 284–303; Theoret. and Math. Phys., 127:2 (2001), 646–663
Citation in format AMSBIB
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\paper Coulomb Gas Representation for Rational Solutions of the Painlev\'e Equations
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\jour Theoret. and Math. Phys.
\yr 2001
\vol 127
\issue 2
\pages 646--663
\crossref{https://doi.org/10.1023/A:1010449603754}
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  • https://www.mathnet.ru/eng/tmf/v127/i2/p284
    • This publication is cited in the following 4 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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