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Reductions and Exact Solutions of Nonlinear Elliptic Systems of a Special Form

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Abstract

We study a nonlinear system of two elliptic differential equations with nonlinearities depending on a product of powers of the unknown functions. Sufficient conditions for the system to be reducible to a single equation are obtained. Some cases are singled out for which we find classes of exact solutions expressed via elementary and harmonic functions and solutions of the Liouville equation.

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Authors and Affiliations

  1. Matrosov Institute of System Dynamics and Control Theory, Siberian Branch, Russian Academy of Sciences, Irkutsk, 664033, Russia

    A. A. Kosov & E. I. Semenov

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

Additional information

Russian Text © The Author(s), 2019, published in Differentsial’nye Uravneniya, 2019, Vol. 55, No. 6, pp. 840–847.

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Kosov, A.A., Semenov, E.I. Reductions and Exact Solutions of Nonlinear Elliptic Systems of a Special Form. Diff Equat 55, 824–831 (2019). https://doi.org/10.1134/S0012266119060090

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  • DOI: https://doi.org/10.1134/S0012266119060090

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