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Teoreticheskaya i Matematicheskaya Fizika, 2012, Volume 173, Number 2, Pages 207–218
DOI: https://doi.org/10.4213/tmf8356 (Mi tmf8356) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Two-sided Darboux transformations

A. B. Shabatab, Z. S. El'kanovaa, A. B. Urusovaa

a Aliev Karachaev--Cherkess State University, Karachaevsk, Russia
b Landau Institute for Theoretical Physics, RAS, Chernogolovka, Moscow Oblast, Russia
Full-text PDF (440 kB) Citations (4)
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DOI: https://doi.org/10.4213/tmf8356
Abstract: We refine the notion of a Darboux transformation for differential operators of an order higher than two and consider commutative rings of differential operators that are invariant under the group of dilations of the independent variable.
Keywords: Darboux transformation, commutative ring of differential operators, third-order Bessel equation.
Received: 04.05.2012
English version:
Theoretical and Mathematical Physics, 2012, Volume 173, Issue 2, Pages 1507–1517
DOI: https://doi.org/10.1007/s11232-012-0130-6
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. B. Shabat, Z. S. El'kanova, A. B. Urusova, “Two-sided Darboux transformations”, TMF, 173:2 (2012), 207–218; Theoret. and Math. Phys., 173:2 (2012), 1507–1517
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf/v173/i2/p207
    • This publication is cited in the following 4 articles:
    1. Yu. Yu. Bagderina, “Higher-order Bessel equations integrable in elementary functions”, J. Math. Sci. (N. Y.), 241:4 (2019), 379–395  mathnet  mathnet  crossref
    2. Sokolov A.V., “Spectral Design For Matrix Hamiltonians: Different Methods of Constructing of a Matrix Intertwining Operator”, J. Phys. A-Math. Theor., 48:8 (2015), 085202  crossref  mathscinet  zmath  adsnasa  isi
    3. F. Kh. Baichorova, “On analogues of third order Bessel function”, Ufa Math. J., 6:1 (2014), 12–17  mathnet  crossref  mathscinet  elib
    4. F. Kh. Baichorova, Z. S. Elkanova, “Commuting differential operators of orders 4 and 6”, Ufa Math. J., 5:3 (2013), 11–19  mathnet  crossref  elib
    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:100
    First page:38
     
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