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

IF 0.8 4区数学 Q2 MATHEMATICS

Differential Equations 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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来源期刊

Differential Equations 数学-数学

CiteScore

1.30

自引率

33.30%

发文量

审稿时长

3-8 weeks

期刊介绍： Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.