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arXiv · 1712.02581

Lie group classification of first-order delay ordinary differential equations

Vladimir A. Dorodnitsyn·Roman Kozlov·Sergey V. Meleshko·Pavel Winternitz
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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 $n$, $0 \leq n \leq 3$. It is shown how exact analytical solutions of invariant DODSs can be obtained using symmetry reduction.

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Vladimir A. Dorodnitsyn, Roman Kozlov, Sergey V. Meleshko, Pavel Winternitz. 2017-12-07. Lie group classification of first-order delay ordinary differential equations. https://doi.org/10.1088/1751-8121%2Faaba91

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