  We discuss various compatibility criteria for overdetermined systems of PDEs
generalizing the approach to formal integrability via brackets of differential
operators. Then we give sufficient conditions that guarantee that a PDE
possessing a Lie algebra of symmetries has invariant solutions with respect to
this Lie algebra. These conditions hold for generic=nondegenerate pairs
(equation,symmetry) in certain dimension range for the Lie algebra. Finally we
discuss models of equations with large symmetry algebras, which eventually lead
to integration in closed form.
