This article is cited in 2 papers

Note on two compatibility criteria: Jacobi–Mayer bracket vs. differential Gröbner basis

B. S. Kruglikov

University of Tromsø

Abstract: We compare two compatibility criteria for overdetermined PDEs: one via geometric theory of differential equations and another via differential algebra approach. Whenever both are applicable, we show that the former is more effective, though in some very special cases they are equivalent.

Keywords: compatibility of differential equations, Jacobi bracket, Mayer bracket, differential Gröbner basis, Kolchin–Ritt algorithm.

Submitted by: V. V. Lychagin
Received: 27.05.2006

Language: English

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