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

This article is cited in 1 scientific paper (total in 1 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

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

Bibliographic databases:

UDC: 517.958
Received: 02.07.2007
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
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  • https://doi.org/10.4213/mzm3914
  • http://mi.mathnet.ru/eng/mz/v85/i3/p421

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    Citing articles on Google Scholar: Russian citations, English citations
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    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  mathnet  crossref  mathscinet  elib
  • Математические заметки Mathematical Notes
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