Lie group classification of first-order delay ordinary differential equations. (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/aaba91
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: A group classification of first-order delay ordinary differential equations (DODEs) accompanied by an equation for the delay parameter (delay relation) is presented. A subset of such systems (delay ordinary differential systems or DODSs), which consists of linear DODEs and solution-independent delay relations, have infinite-dimensional symmetry algebras—as do nonlinear ones that are linearizable by an invertible transformation of variables. Genuinely nonlinear DODSs have symmetry algebras of dimension n, . It is shown how exact analytical solutions of invariant DODSs can be obtained using symmetry reduction.