Electronic Journal of Differential Equations,
Vol. 2000(2000), No. 19, pp. 1-12.

Title: On commuting differential operators

Author: R. Weikard (Univ. of Alabama at Birmingham, Alabama, USA)
         
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 
 $Ly=zy$, $z\in {\Bbb C}$, are meromorphic. In this paper this 
 relationship is explored further by establishing its existence for 
 Gelfand-Dikii systems with rational and simply periodic coefficients. 

Submitted February 22, 2000. Published March 9, 2000.
Math Subject Classifications: 34M05, 37K10, 37K20.
Key Words: Meromorphic solutions; Commuting differential expressions;
           Lax pairs; KdV; Gelfand-Dikii systems.