Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 3 (2007), 045, 17 pages      math-ph/0703038      https://doi.org/10.3842/SIGMA.2007.045
Contribution to the Vadim Kuznetsov Memorial Issue

Spectral Curves of Operators with Elliptic Coefficients

J. Chris Eilbeck a, Victor Z. Enolski b and Emma Previato c
a) The Maxwell Institute and Department of Mathematics, Heriot-Watt University, Edinburgh, UK EH14 4AS
b) Institute of Magnetism, 36 Vernadski Str., Kyiv-142, Ukraine
c) Department of Mathematics and Statistics, Boston University, Boston MA 02215-2411, USA

Received November 21, 2006, in final form February 16, 2007; Published online March 12, 2007

Abstract
A computer-algebra aided method is carried out, for determining geometric objects associated to differential operators that satisfy the elliptic ansatz. This results in examples of Lamé curves with double reduction and in the explicit reduction of the theta function of a Halphen curve.

Key words: (equianharmonic) elliptic integrals; Lamé, Hermite, Halphen equation; theta function.

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