Definition of the differential invariant submodels and an example of its classification

摘要

The differential invariant submodels are constructed by using the differential invariants and the invariant differentiation operators for a subalgebra of the Lie's algebra admitted by the differential equations system. The submodels may be classified for any subalgebra from the optimal system and is given here for the first time. The classification includes the invariant submodels and the partially invariant submodels which have been considered previously. We consider the example of the classification for the subalgebra of rotations admitted by the gas dynamic equations.