This article is cited 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

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.

UDC: 517.958

Received: 02.07.2007
Revised: 09.06.2008

DOI: 10.4213/mzm3914

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

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