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

A. N. Adilkhanov, I. A. Taimanov

Research output: Contribution to journal › Article

1 Citation (Scopus)

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 languageEnglish
Pages (from-to)83-92
Number of pages10
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume42
DOIs
Publication statusPublished - Jan 1 2017

Fingerprint

Discrete Spectrum
Solitons
Mathematical operators
Numerical Study
Korteweg-de Vries equation
Operator
Integrable Systems
Korteweg-de Vries Equation
Spectral Properties
Numerical Scheme
kernel

Keywords

  • Discrete spectrum
  • Galerkin method
  • Schrodinger operator
  • Soliton

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics

Cite this

On numerical study of the discrete spectrum of a two-dimensional Schrödinger operator with soliton potential. / Adilkhanov, A. N.; Taimanov, I. A.

In: Communications in Nonlinear Science and Numerical Simulation, Vol. 42, 01.01.2017, p. 83-92.

Research output: Contribution to journal › Article

Adilkhanov, AN & Taimanov, IA 2017, 'On numerical study of the discrete spectrum of a two-dimensional Schrödinger operator with soliton potential' Communications in Nonlinear Science and Numerical Simulation, vol. 42, pp. 83-92. https://doi.org/10.1016/j.cnsns.2016.04.033
Adilkhanov AN, Taimanov IA. On numerical study of the discrete spectrum of a two-dimensional Schrödinger operator with soliton potential. Communications in Nonlinear Science and Numerical Simulation. 2017 Jan 1;42:83-92. https://doi.org/10.1016/j.cnsns.2016.04.033
Adilkhanov, A. N. ; Taimanov, I. A. / On numerical study of the discrete spectrum of a two-dimensional Schrödinger operator with soliton potential. In: Communications in Nonlinear Science and Numerical Simulation. 2017 ; Vol. 42. pp. 83-92.
@article{8f5e9d0f10f04fbba0cb5aa1802cae2d,
title = "On numerical study of the discrete spectrum of a two-dimensional Schr{\"o}dinger operator with soliton potential",
abstract = "The discrete spectra of certain two-dimensional Schr{\"o}dinger 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 Schr{\"o}dinger operator. The numerical scheme is applicable to a general 2D Schr{\"o}dinger operator with fast decaying potential.",
keywords = "Discrete spectrum, Galerkin method, Schrodinger operator, Soliton",
author = "Adilkhanov, {A. N.} and Taimanov, {I. A.}",
year = "2017",
month = "1",
day = "1",
doi = "10.1016/j.cnsns.2016.04.033",
language = "English",
volume = "42",
pages = "83--92",
journal = "Communications in Nonlinear Science and Numerical Simulation",
issn = "1007-5704",
publisher = "Elsevier",

}

TY - JOUR

T1 - On numerical study of the discrete spectrum of a two-dimensional Schrödinger operator with soliton potential

AU - Adilkhanov, A. N.

AU - Taimanov, I. A.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - 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.

AB - 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.

KW - Discrete spectrum

KW - Galerkin method

KW - Schrodinger operator

KW - Soliton

UR - http://www.scopus.com/inward/record.url?scp=84971265155&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84971265155&partnerID=8YFLogxK

U2 - 10.1016/j.cnsns.2016.04.033

DO - 10.1016/j.cnsns.2016.04.033

M3 - Article

VL - 42

SP - 83

EP - 92

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

SN - 1007-5704

ER -

Access to Document