On the complete integrability of the discrete Nahm equations
نویسندگان
چکیده
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 linebundle 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 linebundle with steps of a fixed size. Some of the implications for hyperbolic monopoles are also discussed. AMS Classification scheme numbers 39A12, 58F07
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