Locality of symmetries generated by nonhereditary, inhomogeneous, and time-dependent recursion operators: a new application for formal symmetries

Using the methods of the theory of formal symmetries, we obtain new easily verifiable sufficient conditions for a recursion operator to produce a hierarchy of local generalized symmetries. An important advantage of our approach is that under certain mild assumptions it allows to bypass the cumbersome check of hereditariness of the recursion operator in question, what is particularly useful for the study of symmetries of newly discovered integrable systems. What is more, unlike the earlier work, the homogeneity of recursion operators and symmetries under a scaling is not assumed as well. An example of nonhereditary recursion operator generating a hierarchy of local symmetries is presented.