Symmetry classification of first integrals for scalar dynamical equations

K. S. Mahomed, E. Momoniat

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

We completely classify the first integrals of scalar non-linear second-order ordinary differential equations (ODEs) in terms of their Lie point symmetries. This is performed by first obtaining the classifying relations between point symmetries and first integrals of scalar non-linear second-order equations which admit one, two and three point symmetries. We show that the maximum number of symmetries admitted by any first integral of a scalar second-order non-linear ODE is one which in turn provides reduction to quadratures of the underlying dynamical equation. We provide physical examples of the generalized Emden-Fowler, Lane-Emden and modified Emden equations.

Original languageEnglish
Pages (from-to)52-59
Number of pages8
JournalInternational Journal of Non-Linear Mechanics
Volume59
DOIs
Publication statusPublished - Jan 2014
Externally publishedYes

Keywords

  • Emden-Fowler
  • First integrals
  • Lane-Emden
  • Modified Emden
  • Non-linear ordinary differential equations
  • Symmetry

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

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