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 journalArticle

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

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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.",
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AU - Taimanov, I. A.

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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

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JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

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