On numerical study of the discrete spectrum of a two-dimensional Schrodinger operator with soliton potential

Abstract

The discrete spectra of certain two-dimensional Schrodinger operators are numerically calculated. These operators have interesting spectral properties, i.e. their kernels are multi-dimensional and the deformations of potentials via the Novikov-Veselov equation (a two-dimensional generalization of the Korteweg-de Vries equation) lead to blowups, and are obtained by the Moutard transformation. The calculations supply the numerical evidence for certain statements on integrable systems related to the 2D Schrodinger operator. The numerical scheme is applicable to a general 2D Schrodinger operator with fast decaying potential.