Generalized integrable hierarchies and Combescure symmetry transformations

Unifying hierarchies of integrable equations are discussed. They are constructed via the generalized Hirota identity. It is shown that the Combescure transformations, known for a long time for the Darboux system and having a simple geometrical meaning, are in fact the symmetry transformations of generalized integrable hierarchies, though the connection with geometry in the general case is not clear. The generalized equation written in terms of invariants of Combescure transformations are the usual integrable equations and their modified partners. The KP - mKP, DS - mDS hierarchies and Darboux system are considered.