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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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\paper Nonlocal Darboux transformation of the~two-dimensional stationary
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  • https://www.mathnet.ru/eng/tmf8942
  • https://doi.org/10.4213/tmf8942
  • https://www.mathnet.ru/eng/tmf/v187/i1/p12
    • This publication is cited in the following 5 articles:
    1. A. G. Kudryavtsev, “On the twofold Moutard transformation of the stationary Schrгöinger equation with axial symmetry”, JETP Letters, 119:7 (2024), 534–537  mathnet  crossref  crossref
    2. Yan Sun, Juan-Juan Wu, Xiao-Yong Wen, “Bifurcation, Traveling Wave Solutions and Dynamical Analysis in the $(2+1)$-Dimensional Extended Vakhnenko–Parkes Equation”, J Nonlinear Math Phys, 31:1 (2024)  crossref
    3. A. G. Kudryavtsev, “On the nonlocal darboux transformation for time-independent axially symmetric Schrödinger and Helmholtz equations”, JETP Letters, 113:6 (2021), 409–412  mathnet  crossref  crossref  isi  elib
    4. A. G. Kudryavtsev, “Exact solutions of the time-independent axially symmetric Schrödinger equation”, JETP Letters, 111:2 (2020), 126–128  mathnet  crossref  crossref  isi  elib
    5. N. Liu, “Optimal system and invariant solutions of a new akns equation with time-dependent coefficients”, Symmetry-Basel, 12:4 (2020), 522  crossref  isi  scopus
    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:95
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