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On the complete integrability of the discrete Nahm equations

Michael K. Murray·Michael A. Singer
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Abstract

The discrete Nahm equations, a system of matrix valued difference equations, arose in the work of Braam and Austin on half-integral mass hyperbolic monopoles. We show that the discrete Nahm equations are completely integrable in a natural sense: to any solution we can associate a spectral curve and a holomorphic line-bundle over the spectral curve, such that the discrete-time DN evolution corresponds to walking in the Jacobian of the spectral curve in a straight line through the line-bundle with steps of a fixed size. Some of the implications for hyperbolic monopoles are also discussed.

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Michael K. Murray, Michael A. Singer. 1999-03-08. On the complete integrability of the discrete Nahm equations. https://doi.org/10.1007/s002200050789

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