SYMMETRIES OF THE KADOMTSEV-PETVIASHVILI EQUATION

Generalized symmetries with arbitary functions of time t for the well known 2 + 1-dimensional integrable model, Kadomtsev-Petviashvili (KP) equation, are found by means of the extended mastersymmetry approach. Then an explicit and simple constructive formula for the symmetries of the KP equation is derived directly from the symmetry definition equa tion, without using complicated recursion operators. All the known sym metries appear as special cases of those obtained in this paper. The g eneral infinite-dimensional Lie algebra constituted by these symmetrie s is also given.