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Second-order delay ordinary differential equations, their symmetries and application to a traffic problem
- Publication Year :
- 2019
-
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 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 {\it first}-order DODSs, here we concentrate on a large class of {\it second}-order ones. We show that within this class the symmetry algebra can be of dimension $n$ with $0 \leq n \leq 6$ for nonlinear DODSs and must be $n=\infty$ 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.<br />arXiv admin note: substantial text overlap with arXiv:1712.02581
- Subjects :
- Statistics and Probability
Pure mathematics
Group (mathematics)
010102 general mathematics
FOS: Physical sciences
General Physics and Astronomy
Lie group
Order (ring theory)
Statistical and Nonlinear Physics
Mathematical Physics (math-ph)
01 natural sciences
010305 fluids & plasmas
Nonlinear system
Mathematics - Classical Analysis and ODEs
Modeling and Simulation
Ordinary differential equation
0103 physical sciences
Homogeneous space
Classical Analysis and ODEs (math.CA)
FOS: Mathematics
0101 mathematics
Symmetry (geometry)
Invariant (mathematics)
Mathematical Physics
Mathematics
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....60d3572b65c1f8bae5686d438ecf03f3