Absence of conductivity-type solitons for the Novikov-Veselov equation at zero energy (Q372465)

The author studies an equation of Novikov-Veselov type at zero energy. For this kind of equation, the following definitions are important: ``sufficiently localized solution'', ``soliton'' (traveling wave) and ``potential of conductivity type''. With these notions, the main result of this paper is formulated and proved: there are no sufficiently localized solitons of conductivity type for the equation of Novikov-Veselov type at zero energy. Another issue addressed in this paper is the problem of scattering data for the two-dimensional Schrödinger equation at zero energy with a potential of conductivity type.