On the discrete spectrum of the nonstationary Schrödinger equation and multipole lumps of the Kadomtsev-Petviashvili I equation (Q1969234)

Schrödinger and Kadomtsev-Petviashvili equations are considered. Mathematical tool is the inverse scattering transform. The existence of infinitely many real and rationally decaying potentials which correspond to a discrete spectrum, whose related eigenfunctions have multiple poles in the spectral parameter, is proved. The resulting localized solutions of the Kadomtsev-Petviashvili I equation behave as a collection of individual lumps with nonuniform dynamics.