Lie group classification of first-order delay ordinary differential equations
Mathematical Physics
2018-05-09 v1 math.MP
Abstract
A group classification of first-order delay ordinary differential equation (DODE) accompanied by an equation for 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 , . It is shown how exact analytical solutions of invariant DODSs can be obtained using symmetry reduction.
Cite
@article{arxiv.1712.02581,
title = {Lie group classification of first-order delay ordinary differential equations},
author = {Vladimir A. Dorodnitsyn and Roman Kozlov and Sergey V. Meleshko and Pavel Winternitz},
journal= {arXiv preprint arXiv:1712.02581},
year = {2018}
}