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

被引：4

作者：

Adilkhanov, A. N. ^{[1
]}

Taimanov, I. A. ^{[2
,3
]}

机构：

[1] Nazarbayev Univ, Natl Lab Astana, 53 Kabanbay Batyr Ave, Astana 010000, Kazakhstan

[2] Sobolev Inst Math, Novosibirsk 630090, Russia

[3] Novosibirsk State Univ, Novosibirsk 630090, Russia

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2017年 / 42卷

关键词：

Schrodinger operator; Discrete spectrum; Galerkin method; Soliton; MOUTARD TRANSFORMATION; EQUATION;

D O I：

10.1016/j.cnsns.2016.04.033

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The discrete spectra of certain two-dimensional Schrodinger 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 Schrodinger operator. The numerical scheme is applicable to a general 2D Schrodinger operator with fast decaying potential. (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：83 / 92

页数：10

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