On the complete integrability of the discrete Nahm equations (Q5938846)

The discrete Nahm (DN) equation is considered. This is a system of matrix-values difference equations introduced by Braam and Austin in the work on half-mass hyperbolic monopoles. The author establishes a correspondence between solutions of this equation and spectral curves \(S\subset{\mathbb P}^1\times{\mathbb P}^1\) with a holomorphic line bundle over it. He shows that the evolution of the DN equation corresponds to the straight line motion on the Jacobian.