𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Symmetry breaking of systems of linear second-order ordinary differential equations with constant coefficients

✍ Scribed by Célestin Wafo Soh

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
174 KB
Volume
15
Category
Article
ISSN
1007-5704

No coin nor oath required. For personal study only.

✦ Synopsis

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 presenting a simple proof of the fact that the dimension of the symmetry Lie algebra of a system of two linear second-order ordinary differential with constant coefficients is either 7, 8 or 15. Also, we establish for the first time that the dimension of the symmetry Lie algebra of a system of three linear secondorder ordinary differential equations with constant coefficients is 10, 12, 13 or 24.

📜 SIMILAR VOLUMES

Comment on “Symmetry breaking of systems
Comment on “Symmetry breaking of systems of linear second-order ordinary differential equations with constant coefficients”
✍ Sergey V. Meleshko 📂 Article 📅 2011 🏛 Elsevier Science 🌐 English ⚖ 167 KB

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.

Linear Second Order Ordinary Differentia
Linear Second Order Ordinary Differential Equations with Nonsmooth Coefficients
✍ Manfred Goebel 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 279 KB

This paper deals with a Dirichlet boundary value problem for a linear second order ordinary differential operator, whose coefficients belong to certain L p -spaces. Its solution is to be understood in the sense of Sobolev, so that the Fredholm alternative holds. The main purpose of this paper is, in

Systems of second-order linear ODE’s wit
Systems of second-order linear ODE’s with constant coefficients and their symmetries
✍ R. Campoamor-Stursberg 📂 Article 📅 2011 🏛 Elsevier Science 🌐 English ⚖ 245 KB

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