We propose a systematic treatment of symmetries of KP integrable systems, including constrained (reduced) KP models ${ \sl cKP}_{ R,M}$, and their multi-component (matrix) generalizations. Any such integrable hierarchy is shown to possess an additional $({ \hat U}(1)\oplus{ \hat { SL}}(M))_{ +} \oplus ({ \hat { SL}}(M+R))_{ -}$ loop-algebra symmetry. Also we provide a systematic construction of the full algebra of Virasoro additional symmetries in the case of constrained KP models which requires a nontrivial modification of the known Orlov-Schulman construction for the general unconstrained KP hierarchy. Multi-component KP hierarchies are identified as ordinary (scalar) one-component KP hierarchies supplemented with the Cartan subalgebra of the additional symmetry algebra, which provides the basis of a new method for construction of soliton-like solutions. Davey-Stewartson and $N$-wave resonant systems arise as symmetry flows of ordinary ${ \sl cKP}_{ R,M}$ hierarchies.
Categories: nlin.SI hep-th
