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

Adilkhanov, A.N.; Taimanov, I.A.; A.N., Adilkhanov

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

Date

2017-01-01

Authors

Adilkhanov, A.N.

A.N., Adilkhanov

Taimanov, I.A.

Publisher

Communications in Nonlinear Science and Numerical Simulation

Abstract

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.

Keywords

Schrodinger operator, Discrete spectrum, Galerkin method, Soliton,

Citation

A.N. Adilkhanov, I.A. Taimanov, On numerical study of the discrete spectrum of a two-dimensional Schrödinger operator with soliton potential, In Communications in Nonlinear Science and Numerical Simulation, Volume 42, 2017, Pages 83-92