Abstract
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.
Original language | English |
---|---|
Pages (from-to) | 83-92 |
Number of pages | 10 |
Journal | Communications in Nonlinear Science and Numerical Simulation |
Volume | 42 |
DOIs | |
Publication status | Published - Jan 1 2017 |
Keywords
- Discrete spectrum
- Galerkin method
- Schrodinger operator
- Soliton
ASJC Scopus subject areas
- Numerical Analysis
- Modelling and Simulation
- Applied Mathematics