General criterion of invariance for integro-differential equations
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.
systems of integro-differential equations
scientific article; zbMATH DE number 5076356