Field theoretical Lie symmetry analysis: The Möbius group, exact solutions of conformal autonomous systems, and predictive model-building

Kyriakos Christodoulides

Research output: Contribution to journalArticle


We study single and coupled first-order differential equations (ODEs) that admit symmetries with tangent vector fields, which satisfy the N-dimensional Cauchy-Riemann equations. In the two-dimensional case, classes of first-order ODEs which are invariant under Möbius transformations are explored. In the N dimensional case we outline a symmetry analysis method for constructing exact solutions for conformal autonomous systems. A very important aspect of this work is that we propose to extend the traditional technical usage of Lie groups to one that could provide testable predictions and guidelines for model-building and model-validation. The Lie symmetries in this paper are constrained and classified by field theoretical considerations and their phenomenological implications. Our results indicate that conformal transformations are appropriate for elucidating a variety of linear and nonlinear systems which could be used for, or inspire, future applications. The presentation is pragmatic and it is addressed to a wide audience.

Original languageEnglish
Pages (from-to)2191-2199
Number of pages9
JournalCommunications in Nonlinear Science and Numerical Simulation
Issue number7
Publication statusPublished - Jul 2014
Externally publishedYes


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