English

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 nn, 0n30 \leq n \leq 3. It is shown how exact analytical solutions of invariant DODSs can be obtained using symmetry reduction.

Keywords

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}
}
R2 v1 2026-06-22T23:10:52.301Z