Electron. J. Diff. Eqns., Vol. 2000(2000), No. 19, pp. 1-12.

On commuting differential operators

R. Weikard

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 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.

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Rudi Weikard
Department of Mathematics
University of Alabama at Birmingham
Birmingham, Alabama 35294-1170, USA
e-mail: rudi@math.uab.edu
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