This article is cited in 1 scientific paper (total in 1 paper)
Algebraic and geometric structures of analytic partial differential equations
O. V. Kaptsovab
a Siberian Federal University, Krasnoyarsk, Russia
b Institute of Computational Modelling, Siberian Branch of the Russian Academy of Sciences, Krasnoyarsk, Russia
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.
compatibility of differential equations, reduction, infinite-dimensional manifold, Gröbner basis
|Ministry of Education and Science of the Russian Federation
|This research was performed under the financial
support of a grant from the Russian government for the conduct of research
under the direction of leading scientists at the Siberian Federal University
(Contract No. 14.U26.31.006) and the Program for Supporting Leading
Scientific Schools (Grant Nos. NSh-544.2012.1 and NSh-6293.2012.9).
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Theoretical and Mathematical Physics, 2016, 189:2, 1592–1608
O. V. Kaptsov, “Algebraic and geometric structures of analytic partial differential equations”, TMF, 189:2 (2016), 219–238; Theoret. and Math. Phys., 189:2 (2016), 1592–1608
Citation in format AMSBIB
\paper Algebraic and geometric structures of analytic partial differential equations
\jour Theoret. and Math. Phys.
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This publication is cited in the following articles:
O. V. Kaptsov, “Intermediate systems and higher-order differential constraints”, J. Sib. Fed. Univ.-Math. Phys., 11:5 (2018), 550–560
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