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

TL;DR

This paper proves that for the KP-2 equation, the direct spectral transform remains nonsingular for all large, real, exponentially decaying potentials, extending previous results limited to small potentials.

Contribution

It establishes the nonsingularity of the direct spectral transform for large potentials, removing the small norm restriction.

Findings

Direct spectral transform is nonsingular for all large potentials.

Previous small norm assumption is no longer necessary.

Results apply to real exponentially decaying potentials.

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.