© Hindawi Publishing Corp. SYMMETRY GROUP ANALYSIS AND INVARIANT SOLUTIONS OF HYDRODYNAMIC-TYPE SYSTEMS

We study point and higher symmetries of systems of the hydrodynamic type with and with-out an explicit dependence on t,x. We consider such systems which satisfy the existence conditions for an infinite-dimensional group of hydrodynamic symmetries which implies lin-earizing transformations for these systems. Under additional restrictions on the systems, we obtain recursion operators for symmetries and use them to construct infinite discrete sets of exact solutions of the studied equations. We find the interrelation between higher sym-metries and recursion operators. Two-component systems are studied in more detail than n-component systems. As a special case, we consider Hamiltonian and semi-Hamiltonian systems of Tsarëv. 2000 Mathematics Subject Classification: 35Q35, 35L40, 76M60