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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

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.

Keywords

Difference Equation Spectral Curve Fixed Size Complete Integrability Natural Sense 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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