Symmetry algebras of third-order ordinary differential equations

Omri Gat*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


The main result of this paper is the complete classification of the third-order ordinary differential equations according to their symmetries. The same classification was done for second order by Tresse ["Dé termination des invariants ponctuels de l'équation différentielle ordinaire du second ordre y"=ω(x,y,y′)," Gekrönte Preisschrift, Hirzel, Leipzig (1896)], and recently for arbitrary order linear ordinary differential equations. The sections preceding the classification consist of a brief description of the concepts and methods along the lines of Krause and Michel [Lecture Notes Phys. 382, 251 (1991)]. These sections also contain some definitions and a table listing the prolongations of a few vector fields. Finally, two appendices give additional information relevant to equations in real variables and describe how some of the results can be easily generalized to higher orders.

Original languageAmerican English
Pages (from-to)2966-2971
Number of pages6
JournalJournal of Mathematical Physics
Issue number9
StatePublished - 1992
Externally publishedYes


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