1. The KM system In two seminal papers [9] for the modern theory of integrable systems Kac and vanMoerbeke introduced the system of o.d.e.’s u̇i = e ui+1 − ei−1 , i = 1, . . . , n, (1) where formally e0 = en+1 = 0. They showed, for example, that this system arises as a finite-dimensional aproximation of the famous KdV equations. Shortly after, Moser [10] showed that this system can be related to...
