Contribution to Book
The Geometrical Study of Differential Equations
Joshua A. Leslie & Thierry P. Robart
American Mathematical Society
This is a brief overview of our work on the theory of group invariant solutions to differential equations. The motivations and applications of this work stem from problems in differential geometry and relativistic field theory. The key feature in our theory is that we allow for non-transverse symmetry group actions, which are very common in applications.
I.M. Anderson, M.E. Fels, and C.G. Torre, Group Invariant Solutions in Mathematical Physics and Differential Geometry, math-ph/0101012, Jan. 2001.