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Sibirskii Matematicheskii Zhurnal, 2005, Volume 46, Number 1, Pages 149–165 (Mi smj947)  

This article is cited in 1 scientific paper (total in 1 paper)

Symmetry operators of a Hartree-type equation with quadratic potential

A. L. Lisoka, A. Yu. Trifonova, A. V. Shapovalovb

a Tomsk Polytechnic University
b Tomsk State University
Full-text PDF (278 kB) Citations (1)
References:
Abstract: We study the symmetry properties of a nonstationary one-dimensional Hartree-type equation with quadratic periodic potential and nonlocal nonlinearity. We find an explicit form of a nonlinear evolution operator for this equation and obtain a solution to a Cauchy problem in the class of semiclassically concentrated functions. We find parametric families of nonlinear symmetry operators of a Hartree-type equation (keeping invariant the set of solutions to this equation). Using the symmetry operators, we construct families of exact solutions to the equation. This approach constructively extends the ideas and methods of group analysis to the case of nonlinear integro-differential equations.
Keywords: nonlinear equations, symmetry operators, evolution operator, Hartree-type equation, semiclassical concentrated states.
Received: 01.12.2003
English version:
Siberian Mathematical Journal, 2005, Volume 46, Issue 1, Pages 119–132
DOI: https://doi.org/10.1007/s11202-005-0013-2
Bibliographic databases:
UDC: 517+517.9
Language: Russian
Citation: A. L. Lisok, A. Yu. Trifonov, A. V. Shapovalov, “Symmetry operators of a Hartree-type equation with quadratic potential”, Sibirsk. Mat. Zh., 46:1 (2005), 149–165; Siberian Math. J., 46:1 (2005), 119–132
Citation in format AMSBIB
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\by A.~L.~Lisok, A.~Yu.~Trifonov, A.~V.~Shapovalov
\paper Symmetry operators of a Hartree-type equation with quadratic potential
\jour Sibirsk. Mat. Zh.
\yr 2005
\vol 46
\issue 1
\pages 149--165
\mathnet{http://mi.mathnet.ru/smj947}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2141310}
\zmath{https://zbmath.org/?q=an:1081.35094}
\transl
\jour Siberian Math. J.
\yr 2005
\vol 46
\issue 1
\pages 119--132
\crossref{https://doi.org/10.1007/s11202-005-0013-2}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000227076100013}
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  • https://www.mathnet.ru/eng/smj/v46/i1/p149
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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