Linear or linearizable first-order delay ordinary differential equations and their Lie point symmetries. (17th April 2018)

• Record Type: Journal Article
• Authors: Dorodnitsyn, Vladimir A; Kozlov, Roman; Meleshko, Sergey V; Winternitz, Pavel
• Is Part Of: Journal of physics. Volume 51:Number 20(2018)
• Publication Date: 2018-04-17
• Subjects: Lie point symmetry -- Lie group classification -- delay ordinary differential equations; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aab3e9
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: A recent article was devoted to an analysis of the symmetry properties of a class of first-order delay ordinary differential systems (DODSs). Here we concentrate on linear DODSs, which have infinite-dimensional Lie point symmetry groups due to the linear superposition principle. Their symmetry algebra always contains a two-dimensional subalgebra realized by linearly connected vector fields. We identify all classes of linear first-order DODSs that have additional symmetries, not due to linearity alone, and we present representatives of each class. These additional symmetries are then used to construct exact analytical particular solutions using symmetry reduction.