We calculate numerically the discrete spectrum of known examples of 2D Schrodinger operators with nontrivial kernels and fast decaying potentials.

We calculate numerically a deformation of the discrete spectrum of the 2D Schrodinger operators whose potentials are given by a blowing up solution of the Novikov–Veselov equation.

We make a conjecture on the behavior of the zero-energy spectrum of the 2D Schrodinger operator under the Moutard transformation.