ANZIAM J.
44 (2002), 83-93
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An integrable system of partial differential equations on the special linear group
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Peter J. Vassiliou
Centre for Mathematics and its Applications
Australian National University
ACT 0200
Australia
On leave from the School of Mathematics and Statistics
University of Canberra
Australia.
pierre@ise.canberra.edu.au
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Abstract
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We give an intrinsic construction of a coupled
nonlinear system consisting of two first-order
partial differential equations in two dependent
and two independent variables which is determined
by a hyperbolic structure on the complex special
linear group regarded as a real Lie group G.
Despite the fact that the system is not Darboux
semi-integrable at first order, the construction
of a family of solutions depending upon two
arbitrary functions, each of one variable, is
reduced to a system of ordinary differential
equations on the 1-jets. The ordinary
differential equations in question are of Lie
type and associated with G.
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