Generalized integrable hierarchies and Combescure symmetry   transformations
  Unifying hierarchies of integrable equations are discussed. They are constructed via 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. 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. 
L.V. Bogdanov (IINS, Landau Institute, Moscow) and B.G. Konopelchenko   (Universita' degli Studi di Lecce)