Group Invariant Solutions without Transversality and the Principle of Symmetric Criticality

I. Anderson, M. Fels, C. Torre

Published 1999-10-09, updated 1999-11-07Version 2

We extend Lie's classical method for finding group invariant solutions to the case of non-transverse group actions. For this extension of Lie's method we identify a local obstruction to the principle of symmetric criticality. Two examples of non-transverse symmetry reductions for the potential form of Maxwell's equations are then examined.