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TMF, 2013, Volume 176, Number 3, Pages 408–416 (Mi tmf8529)  

This article is cited in 4 scientific papers (total in 4 papers)

Faddeev eigenfunctions for two-dimensional Schrödinger operators via the Moutard transformation

I. A. Taimanova, S. P. Tsarevb

a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Siberian Federal University, Krasnoyarsk, Russia

Abstract: We demonstrate how the Moutard transformation of two-dimensional Schrödinger operators acts on the Faddeev eigenfunctions on the zero-energy level and present some explicitly computed examples of such eigenfunctions for smooth rapidly decaying potentials of operators with a nontrivial kernel and for deformed potentials corresponding to blowup solutions of the Novikov–Veselov equation.

Keywords: Schrödinger operator, Faddeev eigenfunction, Moutard transformation, scattering data

DOI: https://doi.org/10.4213/tmf8529

Full text: PDF file (401 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2013, 176:3, 1176–1183

Bibliographic databases:

Document Type: Article
Received: 11.03.2013

Citation: I. A. Taimanov, S. P. Tsarev, “Faddeev eigenfunctions for two-dimensional Schrödinger operators via the Moutard transformation”, TMF, 176:3 (2013), 408–416; Theoret. and Math. Phys., 176:3 (2013), 1176–1183

Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf8529
  • http://mi.mathnet.ru/eng/tmf/v176/i3/p408

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. R. G. Novikov, I. A. Taimanov, “The Moutard transformation and two-dimensional multipoint delta-type potentials”, Russian Math. Surveys, 68:5 (2013), 957–959  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  elib  elib
    2. A. N. Adilkhanov, I. A. Taimanov, “On numerical study of the discrete spectrum of a two-dimensional Schrödinger operator with soliton potential”, Commun. Nonlinear Sci. Numer. Simul., 42 (2017), 83–92  crossref  mathscinet  isi  elib  scopus
    3. M. Music, P. Perry, “Global solutions for the zero-energy Novikov-Veselov equation by inverse scattering”, Nonlinearity, 31:7 (2018), 3413–3440  crossref  mathscinet  zmath  isi  scopus
    4. R. G. Novikov, I. A. Taimanov, “Darboux–Moutard transformations and Poincaré–Steklov operators”, Proc. Steklov Inst. Math., 302 (2018), 315–324  mathnet  crossref  crossref  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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