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Teoreticheskaya i Matematicheskaya Fizika, 2015, Volume 183, Number 3, Pages 342–358
DOI: https://doi.org/10.4213/tmf8760 (Mi tmf8760) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Local algebraic analysis of differential systems

O. V. Kaptsovab

a Institute of Computational Modeling, Siberian Branch, RAS, Krasnoyarsk, Russia
b Siberian Federal University, Krasnoyarsk, Russia
Full-text PDF (477 kB) Citations (2)
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DOI: https://doi.org/10.4213/tmf8760
Abstract: We propose a new approach for studying the compatibility of partial differential equations. This approach is a synthesis of the Riquier method, Gröbner basis theory, and elements of algebraic geometry. As applications, we consider systems including the wave equation and the sine-Gordon equation.
Keywords: compatibility of differential equations, reduction, Gröbner basis.
Funding agency Grant number
Russian Foundation for Basic Research 12-01-00648_а
10-01-00435_а
Ministry of Education and Science of the Russian Federation 14.Y26.31.0006
Received: 02.07.2014
Revised: 09.12.2014
English version:
Theoretical and Mathematical Physics, 2015, Volume 183, Issue 3, Pages 740–755
DOI: https://doi.org/10.1007/s11232-015-0293-z
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: O. V. Kaptsov, “Local algebraic analysis of differential systems”, TMF, 183:3 (2015), 342–358; Theoret. and Math. Phys., 183:3 (2015), 740–755
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf8760
  • https://doi.org/10.4213/tmf8760
  • https://www.mathnet.ru/eng/tmf/v183/i3/p342
    • This publication is cited in the following 2 articles:
    1. Oleg V. Kaptsov, “Ideals generated by differential equations”, Zhurn. SFU. Ser. Matem. i fiz., 13:2 (2020), 170–186  mathnet  crossref
    2. O. V. Kaptsov, “Algebraic and geometric structures of analytic partial differential equations”, Theoret. and Math. Phys., 189:2 (2016), 1592–1608  mathnet  crossref  crossref  mathscinet  adsnasa  isi  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
    Statistics & downloads:
    Abstract page:572
    Full-text PDF :191
    References:74
    First page:61
     
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