Nonsingularity of the direct scattering transform for the KP-2 equation with real exponentially decaying at infinity potential

Abstract

We study the direct spectral transform for the heat equation, associated with the KP-2 equation. We show, that for real nonsingular exponentially decaying at infinity potentials the direct problem is nonsingular for arbitrary large potentials. Earlier this statement was proved only for potentials, satisfying the ``small norm'' assumption.