Conditional differential invariants and equations reducible by means of subalgebras of the Poincaré algebra

Abstract:
We use the concept of the conditional differential invariants for subalgebras of the Poincare algebra to describe equations reducible by means of ansatzes obtained using these subalgebras. We use the theorem by Tsyfra, Zhdanov, Popovych that conditional invariance under some operators is equavalent to reducibility by means of the ansatz obtained using these operators. Our approach considerably extensa the class of equations reducible by means of subalgebras of the Poincare algebra, as compared to description of such equations by means of only absolute differential invariants of these subalgebras. Note that equations reducible by means of some operators may be not invariant under these operators.