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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 › peer-review

Harvard

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

APA

Adilkhanov, A. N., & Taimanov, I. A. (2017). On numerical study of the discrete spectrum of a two-dimensional Schrödinger operator with soliton potential. Communications in Nonlinear Science and Numerical Simulation, 42, 83-92. https://doi.org/10.1016/j.cnsns.2016.04.033

Vancouver

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. doi: 10.1016/j.cnsns.2016.04.033

Author

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.

BibTeX

@article{8beebecfaf8547939faae9c5b41ee43d,
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, MOUTARD TRANSFORMATION, EQUATION",
author = "Adilkhanov, {A. N.} and Taimanov, {I. A.}",
note = "Publisher Copyright: {\textcopyright} 2016 Elsevier B.V..",
year = "2017",
month = jan,
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",

}

RIS

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.

N1 - Publisher Copyright: © 2016 Elsevier B.V..

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

KW - MOUTARD TRANSFORMATION

KW - EQUATION

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

U2 - 10.1016/j.cnsns.2016.04.033

DO - 10.1016/j.cnsns.2016.04.033

M3 - Article

AN - SCOPUS:84971265155

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 -

ID: 10321915