This article is cited in 2 papers

Local algebraic analysis of differential systems

O. V. Kaptsov<sup>ab

a</sup> Institute of Computational Modeling, Siberian Branch, RAS, Krasnoyarsk, Russia
^b Siberian Federal University, Krasnoyarsk, Russia

Abstract: We propose a new approach for studying the compatibility of partial differential equations. This approach is a synthesis of the Riquier method, Gröbner basis theory, and elements of algebraic geometry. As applications, we consider systems including the wave equation and the sine-Gordon equation.

Keywords: compatibility of differential equations, reduction, Gröbner basis.

Received: 02.07.2014
Revised: 09.12.2014

DOI: 10.4213/tmf8760

 English version: Theoretical and Mathematical Physics, 2015, 183:3, 740–755

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