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TMF, 2016, Volume 189, Number 2, Pages 219–238 (Mi tmf9089)  

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

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

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation НШ-544.2012.1
НШ-6293.2012.9
14.Y26.31.0006
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).


DOI: https://doi.org/10.4213/tmf9089

Full text: PDF file (523 kB)
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English version:
Theoretical and Mathematical Physics, 2016, 189:2, 1592–1608

Bibliographic databases:

Received: 26.10.2015
Revised: 02.12.2015

Citation: 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
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\vol 189
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\pages 1592--1608
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. O. V. Kaptsov, “Intermediate systems and higher-order differential constraints”, J. Sib. Fed. Univ.-Math. Phys., 11:5 (2018), 550–560  mathnet  crossref  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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