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J. Sib. Fed. Univ. Math. Phys., 2020, Volume 13, Issue 2, Pages 170–186 (Mi jsfu829)  

Ideals generated by differential equations

Oleg V. Kaptsov

Institute of computational modelling SB RAS, Krasnoyarsk, Russian Federation

Abstract: We propose a new algebraic approach to study compatibility of partial differential equations. The approach uses concepts from commutative algebra, algebraic geometry and Gröbner bases to clarify crucial notions concerning compatibility such as passivity and reducibility. One obtains sufficient conditions for a differential system to be passive and proves that such systems generate manifolds in the jet space. Some examples of constructions of passive systems associated with the sinh-Cordon equation are given.

Keywords: differential rings and ideals, Gröbner bases, partial differential equations.

Funding Agency Grant Number
Russian Foundation for Basic Research 17-01-00332_a
This work was financially supported by the Russian Foundation for Basic Research (Grant no. 17-01-00332-a).


DOI: https://doi.org/10.17516/1997-1397-2020-13-2-170-186

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Bibliographic databases:

UDC: 512.55+517.95
Received: 13.11.2019
Received in revised form: 22.01.2020
Accepted: 06.02.2020
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Citation: Oleg V. Kaptsov, “Ideals generated by differential equations”, J. Sib. Fed. Univ. Math. Phys., 13:2 (2020), 170–186

Citation in format AMSBIB
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\by Oleg~V.~Kaptsov
\paper Ideals generated by differential equations
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2020
\vol 13
\issue 2
\pages 170--186
\mathnet{http://mi.mathnet.ru/jsfu829}
\crossref{https://doi.org/10.17516/1997-1397-2020-13-2-170-186}
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