Linear or linearizable first-order delay ordinary differential equations and their Lie point symmetries

A recent article was devoted to an analysis of the symmetry properties of a class of first-order delay ordinary differential systems (DODSs). Here we concentrate on linear DODSs, which have infinite-dimensional Lie point symmetry groups due to the linear superposition principle. Their symmetry algeb...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2018-05, Vol.51 (20), p.205203
Main Authors: Dorodnitsyn, Vladimir A, Kozlov, Roman, Meleshko, Sergey V, Winternitz, Pavel
Format: Article
Language:English
Subjects:
delay ordinary differential equations
Lie group classification
Lie point symmetry
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Summary:A recent article was devoted to an analysis of the symmetry properties of a class of first-order delay ordinary differential systems (DODSs). Here we concentrate on linear DODSs, which have infinite-dimensional Lie point symmetry groups due to the linear superposition principle. Their symmetry algebra always contains a two-dimensional subalgebra realized by linearly connected vector fields. We identify all classes of linear first-order DODSs that have additional symmetries, not due to linearity alone, and we present representatives of each class. These additional symmetries are then used to construct exact analytical particular solutions using symmetry reduction.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8121/aab3e9