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Izv. Vyssh. Uchebn. Zaved. Mat., 2015, Number 12, Pages 43–54 (Mi ivm9061)  

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

Exact radially-symmetric solutions of a class of nonlinear elliptic systems of equations

A. A. Kosov, E. I. Semyonov

Institute of System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences, 134 Lermontov str., Irkutsk, 664033 Russia

Abstract: We study the system of two equations of elliptic type with two nonlinearities depending on the sum of squares of sought-for functions. We obtain conditions on nonlinearities with which the system is reduced to one equation. We also find parametric families of exact solutions, both radially symmetric, and anisotropic with respect to spatial variables, described by elementary or harmonic functions. In case of controlled nonlinearity we specify wide class of realizable exact solutions expressed via harmonic functions.

Keywords: equations of elliptic type, nonlinear systems, exact solutions.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2015, 59:12, 36–45

UDC: 517.946
Received: 07.05.2014

Citation: A. A. Kosov, E. I. Semyonov, “Exact radially-symmetric solutions of a class of nonlinear elliptic systems of equations”, Izv. Vyssh. Uchebn. Zaved. Mat., 2015, no. 12, 43–54; Russian Math. (Iz. VUZ), 59:12 (2015), 36–45

Citation in format AMSBIB
\Bibitem{KosSem15}
\by A.~A.~Kosov, E.~I.~Semyonov
\paper Exact radially-symmetric solutions of a~class of nonlinear elliptic systems of equations
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2015
\issue 12
\pages 43--54
\mathnet{http://mi.mathnet.ru/ivm9061}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2015
\vol 59
\issue 12
\pages 36--45
\crossref{https://doi.org/10.3103/S1066369X1512004X}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84946406134}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Kosov A.A., Semenov E.I., “Reductions and Exact Solutions of Nonlinear Elliptic Systems of a Special Form”, Differ. Equ., 55:6 (2019), 824–831  crossref  isi
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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