FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2010, VOLUME 16, NUMBER 2, PAGES 67-84

**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**

L. N. Orlova

Abstract

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The geometry of a system of two partial differential equations
containing the first and second partial derivatives of two functions
in two independent variables is studied by using the Cartan method of
invariant forms and the group-theoretic method of extensions and
enclosings due to G. F. Laptev (for finite groups) and
A. M. Vasil'ev (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.

Location: http://mech.math.msu.su/~fpm/eng/k10/k102/k10208h.htm

Last modified: April 5, 2011