Ideals generated by differential equations
Oleg V. Kaptsov
Institute of computational modelling SB RAS, Krasnoyarsk, Russian Federation
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.
differential rings and ideals, Gröbner bases, partial differential equations.
|Russian Foundation for Basic Research
|This work was financially supported by the Russian Foundation for Basic Research (Grant no. 17-01-00332-a).
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Received in revised form: 22.01.2020
Oleg V. Kaptsov, “Ideals generated by differential equations”, J. Sib. Fed. Univ. Math. Phys., 13:2 (2020), 170–186
Citation in format AMSBIB
\paper Ideals generated by differential equations
\jour J. Sib. Fed. Univ. Math. Phys.
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