Geodesic
Algebraic and geometric structures of analytic partial differential equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 189 (2016) no. 2, pp. 219-238 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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O. V. Kaptsov. Algebraic and geometric structures of analytic partial differential equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 189 (2016) no. 2, pp. 219-238. http://geodesic.mathdoc.fr/item/TMF_2016_189_2_a4/

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