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.

UDC: 512.55+517.95

Received: 13.11.2019
Received in revised form: 22.01.2020
Accepted: 06.02.2020

Language: English

DOI: 10.17516/1997-1397-2020-13-2-170-186

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