Integrability of systems of ordinary differential equations via Lie point symmetries

Fatma Al-Kindi; Fazal M. Mahomed; Muhammad Ziad

doi:10.1002/mma.7366

Integrability of systems of ordinary differential equations via Lie point symmetries

Fatma Al-Kindi, Fazal M. Mahomed, Muhammad Ziad^*

^*Corresponding author for this work

Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

The existing literature discusses different strategies to solve a scalar ordinary differential equation using Lie point symmetries. We focus on three of these strategies in order to frame methods for finding solutions of nonlinear systems of ordinary differential equations. These include Lie's integration theorem, method of successive reduction of order, and the method of using the invariants of the admitted symmetry generators. Illustrative examples and those taken from mechanics are presented to highlight the use of these methods.

Original language	English
Pages (from-to)	9373-9392
Number of pages	20
Journal	Mathematical Methods in the Applied Sciences
Volume	44
Issue number	11
DOIs	https://doi.org/10.1002/mma.7366
Publication status	Published - Jul 30 2021

Keywords

nonlinear systems
transformation and reduction of ordinary differential equations and systems

ASJC Scopus subject areas

Mathematics(all)
Engineering(all)

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10.1002/mma.7366

Cite this

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abstract = "The existing literature discusses different strategies to solve a scalar ordinary differential equation using Lie point symmetries. We focus on three of these strategies in order to frame methods for finding solutions of nonlinear systems of ordinary differential equations. These include Lie's integration theorem, method of successive reduction of order, and the method of using the invariants of the admitted symmetry generators. Illustrative examples and those taken from mechanics are presented to highlight the use of these methods.",

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N2 - The existing literature discusses different strategies to solve a scalar ordinary differential equation using Lie point symmetries. We focus on three of these strategies in order to frame methods for finding solutions of nonlinear systems of ordinary differential equations. These include Lie's integration theorem, method of successive reduction of order, and the method of using the invariants of the admitted symmetry generators. Illustrative examples and those taken from mechanics are presented to highlight the use of these methods.

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Integrability of systems of ordinary differential equations via Lie point symmetries

Abstract

Keywords

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