  The Direct and the Inverse Scattering Problems for the heat operator with a
potential being a perturbation of an arbitrary $N$ soliton potential are
formulated. We introduce Jost solutions and spectral data and present their
properties. Then, giving the time evolution of the spectral data, the initial
value problem of the Kadomtsev-Petviashvili II equation for a solution
describing $N$ solitons perturbed by a generic smooth fast decaying potential
is linearized.
