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TMF, 2015, Volume 183, Number 3, Pages 342–358 (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

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


DOI: https://doi.org/10.4213/tmf8760

Full text: PDF file (477 kB)
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English version:
Theoretical and Mathematical Physics, 2015, 183:3, 740–755

Bibliographic databases:

Received: 02.07.2014
Revised: 09.12.2014

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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\paper Local algebraic analysis of differential systems
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  • http://mi.mathnet.ru/eng/tmf/v183/i3/p342

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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
    2. Oleg V. Kaptsov, “Ideals generated by differential equations”, Zhurn. SFU. Ser. Matem. i fiz., 13:2 (2020), 170–186  mathnet  crossref
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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