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Izvestiya: Mathematics, 2021, Volume 85, Issue 3, Pages 343–350
DOI: https://doi.org/10.1070/IM9051 (Mi im9051) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Simple solutions of the Burgers and Hopf equations

V. K. Beloshapkaab

a Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Moscow Center for Fundamental and Applied Mathematics
English version PDF (380 kB) Citations (1)
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DOI: https://doi.org/10.1070/IM9051
Abstract: We describe all solutions of the Burgers equation of analytic complexity not exceeding $1$. It turns out that all such solutions fall into four families of dimensions not exceeding $3$ that are represented by elementary functions. An example of a family of solutions of the Burgers equation of complexity $2$ is given. A similar problem is also solved for the Hopf equation. It turns out that all solutions to the Hopf equation of complexity $1$ form a two-parameter family of fractional-linear functions which coincides with one of the families of solutions of the Burgers equation.
Keywords: analytic complexity, special functions, analytic spectrum.
Funding agency Grant number
Russian Foundation for Basic Research 18-51-41011-Узб-т
The research was financially supported by the Russian Foundation for Basic Research (project no. 18-51-41011-Uzb-t).
Received: 13.04.2020
Revised: 29.06.2020
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2021, Volume 85, Issue 3, Pages 5–12
DOI: https://doi.org/10.4213/im9051
Bibliographic databases:
Document Type: Article
UDC: 517.55+517.923+514.74
MSC: 35A30 (35Q35, 58H05)
Language: English
Original paper language: Russian
Citation: V. K. Beloshapka, “Simple solutions of the Burgers and Hopf equations”, Izv. RAN. Ser. Mat., 85:3 (2021), 5–12; Izv. Math., 85:3 (2021), 343–350
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    References:40
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