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On Exact Solutions of a Multidimensional System of Elliptic Equations with Power-Law Nonlinearities

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Abstract

Equations and systems of elliptic type with power-law nonlinearities are considered. Such equations are found in modeling distributed robotic formations, as well as in chemical kinetics, biology, astrophysics, and many other fields. The problem of constructing multidimensional exact solutions is studied. It is proposed to use a special type of ansatz that reduces the problem to solving systems of algebraic equations. A number of multiparameter families of new exact multidimensional solutions (both radially symmetric and anisotropic) represented by explicit formulas are obtained. Examples are given to illustrate the exact solutions found.

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Funding

This work was supported by the Russian Science Foundation, project no. 22-29-0081.

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Authors and Affiliations

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

    A. A. Kosov & E. I. Semenov

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  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.

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Translated by V. Potapchouck

CONFLICT OF INTEREST. The authors of this work declare that they have no conflicts of interest.

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Kosov, A.A., Semenov, E.I. On Exact Solutions of a Multidimensional System of Elliptic Equations with Power-Law Nonlinearities. Diff Equat 59, 1627–1649 (2023). https://doi.org/10.1134/S0012266123120054

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  • DOI: https://doi.org/10.1134/S0012266123120054

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