Third-order ordinary differential equations y′′′ = f(x, y, y′, y″) with maximal symmetry group. Issue 5 (11th August 2016)

• Record Type: Journal Article
• Authors: Al-Dweik, Ahmad Y.
• Is Part Of: Quaestiones mathematicae. Volume 39:Issue 5(2016)
• Page Start: 595
• Page End: 601
• Publication Date: 2016-08-11
• Subjects: 34A05 -- 34A25 -- 53A55 -- 76M60; Linearization -- third order ODEs -- point transformation -- contact transformation -- Lie symmetries -- relative differential invariants; Mathematics -- Periodicals; 510.5
• DOI: 10.2989/16073606.2015.1113572
• Languages: English
• ISSNs: 1607-3606

Abstract

Abstract: We present here, in compact form, the necessary and sufficient conditions for linearization of third-order ordinary differential equations y''' = f (x, y, y', y'') with maximal symmetry group via point transformation. A simple procedure to construct the point transformation using the isomorphism of the symmetry subalgebra sl(2, ℝ) is also presented. This subalgebra is the semi-simple part of the Levi-Decomposition for the 7-dimensional symmetry algebra.