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SL(n + 1)-invariant equations which reduce to equations of Korteweg-de Vries type

Published online by Cambridge University Press:  14 November 2011

Ian McIntosh
Ian McIntosh
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, U.K.
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Abstract

It is shown how to derive SL(n + 1)-invariant equations which reduce to scalar Lax equations for an operator of order n + 1. The existence of these systems explains the Miura transformation between modified Lax and scalar Lax equations. In particular we study an SL(2)-invariant system with a certain space of solutions lying over the solution space of a Korteweg-de Vries equation described by G. B. Segal and G. Wilson. This enables us to write down some solutions of this SL(2)-invariant system in terms of θ-functions of a hyperelliptic Riemann surface.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 115 , Issue 3-4 , 1990 , pp. 367 - 381
Copyright
Copyright © Royal Society of Edinburgh 1990

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