Meshkov A. G
Oryol State University
302015, Oryol, Komsomolskaia, 95
Mishin S. N
Oryol State University
302015, Oryol, Komsomolskaia, 95
The complete investigation of algebraic algebraic properties is performed for an evolution system of the third order that was obtained in the previous article Kulemin I.V., Meshkov A.G. Symmetry in Nonlinear Math. Phys. V.1, p.115-121, Kyiv, 1997. A zero curvature representation, recursion operator and its inverse are found. A pair of implectic operators are also constructed and it is proved that the system is bi-Hamiltonian one. Three sequences of Lie-Backlund symmetries are constructed. One of them consists of nonlocal symmetries.