M. Ju. Balakhnev
Oryol State University
Department of Physics and Mathematics
95 Komsomolskaya str., 302015, Oryol, Russia
I. V. Kulemin
Oryol State University
Department of Physics and Mathematics
95 Komsomolskaya str., 302015, Oryol, Russia
Differential substitutions of the first and second order for evolution systems of the third order are presented. The systems under consideration are completely integrable systems consisting of one equation of the third order and one equation of the first order. It is established that all found before in the paper of one of the coauthor systems belong to following two classes. The first class consists of systems, equivalent to the Ito system. The second class contains the systems that are equivalent to one of two Drinfeld-Sokolov systems. The main result is more complete, than earlier, list of integrable systems. Also the interrelations between all systems are found.