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Teoreticheskaya i Matematicheskaya Fizika, 2016, Volume 187, Number 1, Pages 12–20
DOI: https://doi.org/10.4213/tmf8942 (Mi tmf8942) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Nonlocal Darboux transformation of the two-dimensional stationary Schrödinger equation and its relation to the Moutard transformation

A. G. Kudryavtsev

Institute of Applied Mechanics, RAS, Moscow, Russia
Full-text PDF (350 kB) Citations (5)
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DOI: https://doi.org/10.4213/tmf8942
Abstract: We consider a nonlocal Darboux transformation of the two-dimensional stationary Schrödinger equation and establish its relation to the Moutard transformation. We show that the Moutard transformation is a special case of the nonlocal Darboux transformation and obtain new examples of solvable two-dimensional stationary Schrödinger operators with smooth potentials as an application of the nonlocal Darboux transformation.
Keywords: Darboux transformation, nonlocal variable, Schrödinger equation.
Received: 30.03.2015
English version:
Theoretical and Mathematical Physics, 2016, Volume 187, Issue 1, Pages 455–462
DOI: https://doi.org/10.1134/S0040577916040024
Bibliographic databases:
Document Type: Article
PACS: 02.30.Jr, 02.30.Ik, 03.65.Ge
Language: Russian
Citation: A. G. Kudryavtsev, “Nonlocal Darboux transformation of the two-dimensional stationary Schrödinger equation and its relation to the Moutard transformation”, TMF, 187:1 (2016), 12–20; Theoret. and Math. Phys., 187:1 (2016), 455–462
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:87
    First page:40
     
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