Group foliation and noninvariant solutions of the heavenly equation
Abstract
The main physical results of this paper are new exact analytical solutions of the heavenly equation, of importance in the general theory of relativity. These solutions are not invariant under any subgroup of the symmetry group of the equation. The main mathematical result is a new method of obtaining noninvariant solutions of partial differential equations with infinitedimensional symmetry groups. The method involves the compatibility of the given equations with a differential constraint, which is automorphic under a specific symmetry subgroup, the latter acting transitively on the submanifold of the common solutions. By studying the integrability of the resulting conditions, one can provide an explicit foliation of the entire solution manifold of the considered equations.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 November 2001
 DOI:
 10.1088/03054470/34/43/310
 arXiv:
 arXiv:mathph/0108004
 Bibcode:
 2001JPhA...34.9243M
 Keywords:

 Mathematical Physics;
 Mathematics  Group Theory;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 35Q75;
 57S20
 EPrint:
 32 pages, Latex, corrected typos, submitted to J. Phys. A: Math. Gen. on April 13, 2001