|
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.
Received: 13.11.2019 Received in revised form: 22.01.2020 Accepted: 06.02.2020
Citation:
Oleg V. Kaptsov, “Ideals generated by differential equations”, J. Sib. Fed. Univ. Math. Phys., 13:2 (2020), 170–186
Linking options:
https://www.mathnet.ru/eng/jsfu829 https://www.mathnet.ru/eng/jsfu/v13/i2/p170
|
Statistics & downloads: |
Abstract page: | 117 | Full-text PDF : | 64 | References: | 13 |
|