RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 2009, Volume 85, Issue 3, Pages 421–432 (Mi mz3914)

The Geometry of a Quasilinear System of Two Partial Differential Equations Containing the First and the Second Partial Derivatives of Two Functions in Two Independent Variables

L. N. Orlova

Moscow State University of Civil Engineering

Abstract: The geometry of the system of two partial differential equations containing the first and second partial derivatives of two functions in two independent variables is studied by using Élie Cartan's method of invariant forms and the group-theoretic method of extensions and enclosings due to G. F. Laptev (for finite groups) and A. M. Vasilev (for infinite groups). Systems of quasilinear equations with the first and second partial derivatives of two functions $u$ and $v$ in two independent variables $x$ and $y$ are classified.

Keywords: geometry of partial differential equations, quasilinear partial differential system, integral manifold, point transformation group, characteristic

DOI: https://doi.org/10.4213/mzm3914

Full text: PDF file (414 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2009, 85:3, 409–419

Bibliographic databases:

UDC: 517.958
Revised: 09.06.2008

Citation: L. N. Orlova, “The Geometry of a Quasilinear System of Two Partial Differential Equations Containing the First and the Second Partial Derivatives of Two Functions in Two Independent Variables”, Mat. Zametki, 85:3 (2009), 421–432; Math. Notes, 85:3 (2009), 409–419

Citation in format AMSBIB
\Bibitem{Orl09} \by L.~N.~Orlova \paper The Geometry of a Quasilinear System of Two Partial Differential Equations Containing the First and the Second Partial Derivatives of Two Functions in Two Independent Variables \jour Mat. Zametki \yr 2009 \vol 85 \issue 3 \pages 421--432 \mathnet{http://mi.mathnet.ru/mz3914} \crossref{https://doi.org/10.4213/mzm3914} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2548049} \zmath{https://zbmath.org/?q=an:1179.35036} \elib{http://elibrary.ru/item.asp?id=15302285} \transl \jour Math. Notes \yr 2009 \vol 85 \issue 3 \pages 409--419 \crossref{https://doi.org/10.1134/S0001434609030110} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000266561100011} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-69949113604} 

• http://mi.mathnet.ru/eng/mz3914
• https://doi.org/10.4213/mzm3914
• http://mi.mathnet.ru/eng/mz/v85/i3/p421

 SHARE:

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. L. N. Orlova, “The geometry of a quasilinear system of two partial differential equations containing the first and second partial derivatives of two functions in two independent variables”, J. Math. Sci., 177:5 (2011), 692–704
•  Number of views: This page: 246 Full text: 63 References: 29 First page: 10