SOME NEW METHODS AND RESULTS IN THE THEORY OF (2-DIMENSIONAL INTEGRABLE EQUATIONS(1))

The general resolvent scheme for solving nonlinear integrable evolutio n equations is formulated. Special attention is paid to the problem of nontrivial dressing and the corresponding transformation of spectral data. The Kadomtsev-Petviashvili equation is considered as the standar d example of integrable models in 2 + 1 dimensions. Properties of the solution u(t, z, y) of the Kadomtsev-Petviashvili I equation as well a s the corresponding Jest solutions and spectral data with given initia l data u(0, x, y) belonging to the Schwartz space are presented.