Communications in Mathematical Physics

, Volume 210, Issue 2, pp 497–519 | Cite as

On the Complete Integrability of the Discrete Nahm Equations

  • Michael K. Murray
  • Michael A. Singer


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.


Difference Equation Spectral Curve Fixed Size Complete Integrability Natural Sense 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Michael K. Murray
    • 1
  • Michael A. Singer
    • 2
  1. 1.Department of Pure Mathematics, University of Adelaide, Adelaide, SA 5005, AustraliaAU
  2. 2.Department of Mathematics and Statistics, James Clerk Maxwell Building, University of Edinburgh,¶Edinburgh EH9 3JZ, UKUK

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