Linearisation of a second-order nonlinear ordinary differential equation

IF 0.6 Q3 ENGINEERING, MULTIDISCIPLINARY

Acta Polytechnica Pub Date : 2023-03-02 DOI:10.14311/ap.2023.63.0019

A. Maharaj, P. Leach, M. Govender, David P. Day

引用次数: 0

Abstract

We analyse nonlinear second-order differential equations in terms of algebraic properties by reducing a nonlinear partial differential equation to a nonlinear second-order ordinary differential equation via the point symmetry f(v)∂v. The eight Lie point symmetries obtained for the second-order ordinary differential equation is of maximal number and a representation of the sl(3,R) algebra. We extend this analysis to a more general nonlinear second-order differential equation and we obtain similar interesting algebraic properties.

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二阶非线性常微分方程的线性化

我们用代数性质分析非线性二阶微分方程，通过点对称性f（v）⏴v将非线性偏微分方程简化为非线性二阶常微分方程。二阶常微分方程得到的八个李点对称性是极大数，是sl（3，R）代数的一个表示。我们将这种分析扩展到一个更一般的非线性二阶微分方程，并获得了类似的有趣的代数性质。

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

Acta Polytechnica ENGINEERING, MULTIDISCIPLINARY-

CiteScore

1.90

自引率

12.50%

发文量

审稿时长

24 weeks

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