General criterion of invariance for integro-differential equations
type: Item
instance of: scholarly article
title: General criterion of invariance for integro-differential equations
zbMATH Open document ID: 1116.45005
DOI: 10.1016/S0034-4877(04)80017-X
author: Zygmunt Jacek Zawistowski
published in: Reports on Mathematical Physics
publication date: 2006-11-27T00:00:00Z
review text: The author discusses a method of determining symmetry groups of point transformations for systems of integro-differential equations with the domains of integration possibly depending on external variables and thus moving under point transformations. The approach is based on \textit{L. V. Ovsiannikov}'s [Group analysis of differential equations. (1982; Zbl 0485.58002)] method of lifting the group of transformations to a jet bundle, and the author manages to derive a necessary condition for invariance of the discussed integro-differential equations under the introduced point transformation. In the discussion, the author compares the criterion with other methods and notes that particular versions of it were used earlier for the Vlasow-Maxwell equation.
reviewed by: Jacek Banasiak
Mathematics Subject Classification ID: 45K05
Mathematics Subject Classification ID: 58J70
zbMATH DE Number: 5076356
zbMATH Keywords: Lie groups
zbMATH Keywords: symmetries
zbMATH Keywords: invariance
zbMATH Keywords: systems of integro-differential equations
zbMATH Keywords: symmetry groups
zbMATH Keywords: point transformations
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5076356