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On some geometry associated with a generalised Toda lattice

Published online by Cambridge University Press:  17 April 2009

P.J. Vassiliou
P.J. Vassiliou
Affiliation:
Faculty of Information Sciences and EngineeringUniversity of CanberraBelconnen ACT 2616, Australia
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We define the notion of Darboux integrability for linear second order partial differential operators,

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We then build on certain geometric results of E. Vessiot related to the theory of Monge characteristics to show that the Darboux integrable operators L can be used to obtain a solution of the A2 Toda field theory. This solution is parametrised by four arbitrary functions. The approach presented in this paper thereby represents an alternative means of linearising the A2 Toda equations and may be contrasted with the known linearisation via the Lax pair.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 49 , Issue 3 , June 1994 , pp. 439 - 462
Copyright
Copyright © Australian Mathematical Society 1994

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