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

Pub Date : 2023-12-01 DOI:10.1134/s0012266123120054

引用次数: 0

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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论带有幂律非线性的多维椭圆方程系统的精确解

摘要本研究考虑了具有幂律非线性的椭圆方程和系统。分布式机器人编队建模以及化学动力学、生物学、天体物理学和许多其他领域都存在此类方程。研究了构建多维精确解的问题。建议使用一种特殊类型的解析，将问题简化为求解代数方程系统。通过明确的公式得到了一些新的多维精确解（包括径向对称和各向异性）的多参数族。举例说明了所发现的精确解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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