Advances in Mathematics
By developing the Tanaka theory for rank 2 distributions, we completely classify classical Monge equations having maximal finite-dimensional symmetry algebras with fixed (albeit arbitrary) pair of its orders. Investigation of the corresponding Tanaka algebras leads to a new Lie-Backlund theorem. We prove that all flat Monge equations are successive integrable extensions of the Hilbert-Cartan equation. Many new examples are provided.
Ian Anderson, Boris Kruglikov, Rank 2 distributions of Monge equations: Symmetries, equivalences, extensions, Advances in Mathematics, Volume 228, Issue 3, 20 October 2011, Pages 1435-1465, ISSN 0001-8708, 10.1016/j.aim.2011.06.019.