  The problem of computing differential constraints for a family of evolution
PDEs is discussed from a constructive point of view. A new method, based on the
existence of generalized characteristics for evolution vector fields, is
proposed in order to obtain explicit differential constraints for PDEs
belonging to this family. Several examples, with applications in non-linear
stochastic filtering theory, stochastic perturbation of soliton equations and
non-isospectral integrable systems, are discussed in detail to verify the
effectiveness of the method.
