We show that the structure of the Lie symmetry algebra of a system of n linear secondorder ordinary differential equations with constant coefficients depends on at most n À 1 parameters. The tools used are Jordan canonical forms and appropriate scaling transformations. We put our approach to test by
Comment on “Symmetry breaking of systems of linear second-order ordinary differential equations with constant coefficients”
✍ Scribed by Sergey V. Meleshko
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 167 KB
- Volume
- 16
- Category
- Article
- ISSN
- 1007-5704
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✦ Synopsis
The present paper corrects the way of using Jordan canonical forms for studying the symmetry structures of systems of linear second-order ordinary differential equations with constant coefficients applied in [1]. The approach is demonstrated for a system consisting of two equations.
📜 SIMILAR VOLUMES
Starting from the study of the symmetries of systems of 4 second-order linear ODEs with constant real coefficients, we determine the dimension and generators of the symmetry algebra for systems of \(n\) equations described by a diagonal Jordan canonical form. We further prove that some dimensions be