Email this article Reductions and Exact Solutions of Nonlinear Elliptic Systems of a Special Form
- Authors: Kosov A.A.1, Semenov E.I.1
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Affiliations:
- Matrosov Institute of System Dynamics and Control Theory, Siberian Branch
- Issue: Vol 55, No 6 (2019)
- Pages: 824-831
- Section: Partial Differential Equations
- URL: https://journals.rcsi.science/0012-2661/article/view/155049
- DOI: https://doi.org/10.1134/S0012266119060090
- ID: 155049
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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.
About the authors
A. A. Kosov
Matrosov Institute of System Dynamics and Control Theory, Siberian Branch
Author for correspondence.
Email: kosov_idstu@mail.ru
Russian Federation, Irkutsk, 664033
E. I. Semenov
Matrosov Institute of System Dynamics and Control Theory, Siberian Branch
Author for correspondence.
Email: edwseiz@gmail.com
Russian Federation, Irkutsk, 664033
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