A generalization of λ-symmetry reduction for systems of ODEs: σ-symmetries

We consider a deformation of the prolongation operation, defined on sets of vector fields and involving a mutual interaction in the definition of prolonged ones. This maintains the 'invariants by differentiation' property, and can hence be used to reduce ODEs satisfying suitable invariance...

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Bibliographic Details
Published inJournal of physics. A, Mathematical and theoretical Vol. 45; no. 35; pp. 355205 - 355233
Main Authors Cicogna, G, Gaeta, G, Walcher, S
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 07.09.2012
IOP
Subjects
differential invariants
Exact sciences and technology
nonlinear systems
Physics
reduction
symmetry of differential equations
Invariant
Deformation
Invariance
Vector fields
Differential equations
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Summary:We consider a deformation of the prolongation operation, defined on sets of vector fields and involving a mutual interaction in the definition of prolonged ones. This maintains the 'invariants by differentiation' property, and can hence be used to reduce ODEs satisfying suitable invariance conditions in a fully algorithmic way, similarly to what happens for standard prolongations and symmetries.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/45/35/355205