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Matematicheskie Zametki, 2009, Volume 85, Issue 3, Pages 421–432
DOI: https://doi.org/10.4213/mzm3914 (Mi mzm3914) 		 
This article is cited in 2 scientific papers (total in 2 papers)

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
Full-text PDF (414 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm3914
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.
Received: 02.07.2007
Revised: 09.06.2008
English version:
Mathematical Notes, 2009, Volume 85, Issue 3, Pages 409–419
DOI: https://doi.org/10.1134/S0001434609030110
Bibliographic databases:
UDC: 517.958
Language: Russian
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
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  • https://www.mathnet.ru/eng/mzm3914
  • https://doi.org/10.4213/mzm3914
  • https://www.mathnet.ru/eng/mzm/v85/i3/p421
    • This publication is cited in the following 2 articles:
    1. L. N. Orlova, “Geometry of a quasilinear system of two partial differential equations of the 1st and 2nd order in two functions of two independent variables”, J Math Sci, 174:5 (2011), 641  crossref
    2. 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  mathnet  crossref  mathscinet  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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