Differential invariants and construction of conditionally invariant equations. (English) Zbl 1038.58049
Nikitin, A. G. (ed.) et al., Proceedings of the fourth international conference on symmetry in nonlinear mathematical physics, Kyïv, Ukraine, July 9–15, 2001. Part 1. Dedicated to the 200th anniversary of M. Ostrohrads’kyi. Kyïv: Institute of Mathematics of NAS of Ukraine (ISBN 966-02-2486-9). Proc. Inst. Math. Natl. Acad. Sci. Ukr., Math. Appl. 43(1), 256-262 (2002).
A new concept of conditional differential invariants is introduced that allows the description of equations invariants with respect to an operator under a certain condition. Finding a basis of conditional differential invariants allows the description of all equations having the same conditional invariance property, and the description of all equations reducible by means of a certain Ansatz. An example of conditional invariants of the projective operator is given the description of all Poincaré-invariant equations having the same conditional or hidden symmetry property as the nonlinear wave equation with cubic nonlinearity possible.
For the entire collection see [Zbl 0989.00037].
For the entire collection see [Zbl 0989.00037].
Reviewer: V. M. Boyko (Kyïv)
MSC:
| 58J70 | Invariance and symmetry properties for PDEs on manifolds |
| 53A55 | Differential invariants (local theory), geometric objects |
| 58J72 | Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds |
| 35L05 | Wave equation |
