On commuting differential operators - R. Weikard (Electronic Journal of Differential Equations, 2000)
The theory of commuting linear differential expressions has received a lot of attention since Lax presented his description of the KdV hierarchy by Lax pairs $(P,L)$. Gesztesy and the present author have established a relationship of this circle of ideas with the property that all solutions of the differential equations $Ly=zy$, $zin Bbb C$, are meromorphic. In this paper this relationship is explored further by establishing its existence for Gelfand-Dikii systems with rational and simply periodic coefficients.