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The computational approach to commuting ordinary differential operators of orders six and nine

Published online by Cambridge University Press:  17 February 2009

Geoff A. Latham
Geoff A. Latham
Affiliation:
Centre for Mathematics and its Applications, ANU, GPO Box 4, Canberra ACT 2601.
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Abstract

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Entirely elementary methods are employed to determine explicit formulae for the coefficients of commuting ordinary differential operators of orders six and nine which correspond to an elliptic curve. These formulae come from solving the nonlinear ordinary differential equations which are equivalent to the commutativity condition. Most solutions turn out to be rational expressions in one or two arbitrary functions and their derivatives. The corresponding Burchnall-Chaundy curves are computed.

Type
Research Article
Information
The ANZIAM Journal , Volume 35 , Issue 4 , April 1994 , pp. 399 - 419
Copyright
Copyright © Australian Mathematical Society 1994

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