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Teoreticheskaya i Matematicheskaya Fizika, 2020, Volume 205, Number 1, Pages 3–22
DOI: https://doi.org/10.4213/tmf9940 (Mi tmf9940) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Binary relations, Bäcklund transformations, and wave packet propagation

V. V. Zharinov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
Full-text PDF (545 kB) Citations (1)
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DOI: https://doi.org/10.4213/tmf9940
Abstract: We propose a mathematical apparatus based on binary relations that expands the possibility of traditional analysis applied to problems in mathematical and theoretical physics. We illustrate the general constructions with examples with an algebraic description of Bäcklund transformations of nonlinear systems of partial differential equations and the dynamics of wave packet propagation.
Keywords: binary relation, related sets, related endomorphisms, related morphisms, related categories, related functors, differential relation, related symmetries, Bäcklund transformation, fuzzy category, wave packet, dispersion.
Received: 24.05.2020
Revised: 24.05.2020
English version:
Theoretical and Mathematical Physics, 2020, Volume 205, Issue 1, Pages 1245–1263
DOI: https://doi.org/10.1134/S0040577920100013
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. V. Zharinov, “Binary relations, Bäcklund transformations, and wave packet propagation”, TMF, 205:1 (2020), 3–22; Theoret. and Math. Phys., 205:1 (2020), 1245–1263
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf9940
  • https://doi.org/10.4213/tmf9940
  • https://www.mathnet.ru/eng/tmf/v205/i1/p3
    • This publication is cited in the following 1 articles:
    1. V. V. Zharinov, “Dynamics of wave packets in the functional mechanics”, Int. J. Mod. Phys. A, 37:20 (2022), 2243027–10  mathnet  crossref  mathscinet
    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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    Abstract page:296
    Full-text PDF :52
    References:80
    First page:13
     
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