The discrete spectra of certain two-dimensional Schrödinger operators are numerically calculated. These operators are obtained by the Moutard transformation and have interesting spectral properties: 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. The calculations supply the numerical evidence for some statements about the integrable systems related to a 2D Schrödinger operator. The numerical scheme is applicable to a general 2D Schrödinger operator with fast decaying potential.
|Number of pages||10|
|Journal||Communications in Nonlinear Science and Numerical Simulation|
|Publication status||Published - 1 Jan 2017|
- Discrete spectrum
- Galerkin method
- Schrodinger operator
- MOUTARD TRANSFORMATION