An Integrable System of Partial Differential Equations on the Complex Projective Group

Research Report MRR00-023

An Integrable System of Partial Differential Equations on the Complex Projective Group

Peter J. Vassiliou

Abstract: 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 Lie group of linear fractional transformations of the complex plane, 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 which is of Lie type and associated to G.

Download paper:	PDF file (93K)
	gzipped PostScript file (30K)

This service is maintained by the Mathematical Sciences Institute (MSI)
Comments to webmaster@maths.anu.edu.au URL: http://wwwmaths.anu.edu.au/