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.
A generalization of lambda-symmetry reduction for systems of ODEs: sigma-symmetries / G. Cicogna, G. Gaeta, S. Walcher. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - 45:35(2012).
A generalization of lambda-symmetry reduction for systems of ODEs: sigma-symmetries
G. GaetaSecondo
;
2012
Abstract
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.
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