Second-order delay ordinary differential equations, their symmetries and application to a traffic problem. (22nd February 2021)

• Record Type: Journal Article
• Authors: Dorodnitsyn, Vladimir A; Kozlov, Roman; Meleshko, Sergey V; Winternitz, Pavel
• Is Part Of: Journal of physics. Volume 54:Number 10(2021)
• Publication Date: 2021-02-22
• Subjects: delay ordinary differential equation -- Lie group classification -- particular solutions for traffic flow model; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/abdc81
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: This article is the third in a series, the aim of which is to use Lie group theory to obtain exact analytic solutions of delay ordinary differential systems (DODSs). Such a system consists of two equations involving one independent variable x and one dependent variable y . As opposed to ordinary differential equations (ODEs) the variable x figures in more than one point (we consider the case of two points, x and x − ). The dependent variable y and its derivatives figure in both x and x − . Two previous articles were devoted to first -order DODSs, here we concentrate on a large class of second -order ones. We show that within this class the symmetry algebra can be of dimension n with 0 ⩽ n ⩽ 6 for nonlinear DODSs and must be infinite-dimensional for linear or linearizable ones. The symmetry algebras can be used to obtain exact particular group invariant solutions. As a specific application we present some exact solutions of a DODS model of traffic flow.