Symmetries of PDE systems and correspondences between jet spaces
type: Item
instance of: scholarly article
title: Symmetries of PDE systems and correspondences between jet spaces
zbMATH Open document ID: 1216.58011
author: Juan-Miguel Gracia
published in: Journal of Mathematical Analysis and Applications
publication date: 2011-03-14T00:00:00Z
review text: For a smooth manifold \(M\) let \(J^k_mM\) be the space of \(k\)-jets of \(m\)-dimensional (locally closed) submanifolds of \(M\). A system of PDEs is considered as \({\mathcal R}\subseteq J^k_mM\). We can associate with \({\mathcal R}\) another system \({\mathcal R}^*\subseteq T^*M\) with only one unknown function. The present paper deals with the very interesting relationship between different types of symmetries of \({\mathcal R}\) and \({\mathcal R}^*\). One of the main tools is the theory of jet spaces in the Weil bundles framework.
Mathematics Subject Classification ID: 58J70
Mathematics Subject Classification ID: 35A30
Mathematics Subject Classification ID: 58A20
zbMATH DE Number: 5865633
zbMATH Keywords: jet
zbMATH Keywords: contact element
zbMATH Keywords: Lie correspondence
zbMATH Keywords: system of partial differential equations
zbMATH Keywords: symmetry
zbMATH Keywords: internal symmetry
zbMATH Keywords: invariant solution
reviewed by: Mircea Crasmareanu
MaRDI profile type: Publication
full work available at URL: j.jmaa.2010.12.007
OpenAlex ID: W2069368865
cites work: A transformation of PDE systems related to the drach theorem.
cites work: Q3416937
cites work: Some Canonical Structures of Cartan Planes in Jet Spaces and Applications
cites work: Q3435468
cites work: Exterior differential systems with symmetry
cites work: Internal, external, and generalized symmetries
cites work: Q4238949
cites work: Q5805471
cites work: Q4407753
cites work: Q4660508
cites work: Q4329389
cites work: Q3998623
cites work: LOCAL CLASSIFICATION OF NON-LINEAR FIRST ORDER PARTIAL DIFFERENTIAL EQUATIONS
cites work: Weil bundles and jet spaces
cites work: Integrability of Lie equations and pseudogroups
cites work: A remark on Goldschmidt's theorem on formal integrability
cites work: On the finiteness of differential invariants.
cites work: Q5822224
DOI: 10.1016/J.JMAA.2010.12.007
description: scientific article; zbMATH DE number 5865633