Integrability of systems of ordinary differential equations via Lie point symmetries

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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 languageEnglish
Pages (from-to)9373-9392
Number of pages20
JournalMathematical Methods in the Applied Sciences
Issue number11
Publication statusPublished - Apr 6 2021


  • nonlinear systems
  • transformation and reduction of ordinary differential equations and systems

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)


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