We demonstrate how the Moutard transformation of two-dimensional Schrodinger operators acts on the Faddeev eigenfunctions on the zero energy level and present some explicitly computed examples of such eigenfunctions for smooth fast decaying potential
s of operators with non-trivial kernel and for deformed potentials which correspond to blowing up solutions of the Novikov-Veselov equation.
Using Moutard transformations we show how explicit examples of two-dimensional Schroedinger operators with fast decaying potential and multidimensional $L_2$-kernel may be constructed
