Group Invariant Solutions without Transversality and the Principle of Symmetric Criticality
arXiv:math-ph/9910014 · doi:10.1007/s002200000215
Abstract
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.
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