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On multidimensional exact solutions of a nonlinear system of two equations of elliptic type

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Abstract

We study a nonlinear system of two differential equations of elliptic type and of special form. We obtain conditions under which the system can be reduced to a single equation. We find classes of radially symmetric and anisotropic exact solutions given by elementary and harmonic functions.

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Authors and Affiliations

  1. Matrosov Institute for System Dynamics and Control Theory of Siberian Branch of Russian Academy of Sciences, Irkutsk, Russia

    E. I. Semenov & A. A. Kosov

Authors
  1. E. I. Semenov
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  2. A. A. Kosov
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Correspondence to E. I. Semenov.

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Original Russian Text © E.I. Semenov, A.A. Kosov, 2015, published in Differentsial’nye Uravneniya, 2015, Vol. 51, No. 2, pp. 229–239.

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Semenov, E.I., Kosov, A.A. On multidimensional exact solutions of a nonlinear system of two equations of elliptic type. Diff Equat 51, 232–242 (2015). https://doi.org/10.1134/S0012266115020081

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  • DOI: https://doi.org/10.1134/S0012266115020081

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