ANZIAM  J.  44 (2002), 83-93
An integrable system of partial differential equations on the special linear group

Peter J. Vassiliou
  Centre for Mathematics and its Applications
  Australian National University
  ACT 0200
  On leave from the School of Mathematics and Statistics
  University of Canberra

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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