Lie group classification of first-order delay ordinary differential equations

A group classification of first-order delay ordinary differential equations (DODEs) accompanied by an equation for the 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...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2018-05, Vol.51 (20), p.205202
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 group classification of first-order delay ordinary differential equations (DODEs) accompanied by an equation for the 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, . It is shown how exact analytical solutions of invariant DODSs can be obtained using symmetry reduction.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8121/aaba91