Electronic Journal of Differential Equations (Mar 2000)
On commuting differential operators
Abstract
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.
