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An integrable system of partial differential equations on the special linear group

Published online by Cambridge University Press:  17 February 2009

Peter J. Vassiliou
Peter J. Vassiliou
Affiliation:
Centre for Mathematics and its Applications, Australian National University, ACT 0200, Australia; e-mail: pierre@ise.canberra.edu.au. On leave from the School of Mathematics and Statistics, University of Canberra, ACT, Australia.
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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.

Type
Research Article
Information
The ANZIAM Journal , Volume 44 , Issue 1 , July 2002 , pp. 83 - 93
Copyright
Copyright © Australian Mathematical Society 2002

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