This article is cited in 1 paper

Algebraic and geometric structures of analytic partial differential equations

O. V. Kaptsov<sup>ab

a</sup> Siberian Federal University, Krasnoyarsk, Russia
^b Institute of Computational Modelling, Siberian Branch of the Russian Academy of Sciences, Krasnoyarsk, Russia

Abstract: We study the problem of the compatibility of nonlinear partial differential equations. We introduce the algebra of convergent power series, the module of derivations of this algebra, and the module of Pfaffian forms. Systems of differential equations are given by power series in the space of infinite jets. We develop a technique for studying the compatibility of differential systems analogous to the Gröbner bases. Using certain assumptions, we prove that compatible systems generate infinite manifolds.

Keywords: compatibility of differential equations, reduction, infinite-dimensional manifold, Gröbner basis.

Received: 26.10.2015
Revised: 02.12.2015

DOI: 10.4213/tmf9089

 English version: Theoretical and Mathematical Physics, 2016, 189:2, 1592–1608

Bibliographic databases:

• 
• 
• 
• 
•