Faddeev eigenfunctions for two-dimensional Schrödinger operators via the Moutard transformation

We demonstrate how the Moutard transformation of two-dimensional Schrödinger operators acts on the Faddeev eigenfunctions on the zero-energy level and present some explicitly computed examples of such eigenfunctions for smooth rapidly decaying potentials of operators with a nontrivial kernel and for deformed potentials corresponding to blowup solutions of the Novikov–Veselov equation.