Abstract
Rudi Weikard
Department of Mathematics
University of Alabama at Birmingham
Birmingham, AL 35294-1170
USA
Title: Commuting Differential Operators and Integrable Systems.
Abstract: According to P. Lax certain integrable partial differential equations,
notably the KdV equation, may be expressed as $L_t=[P,L]$ where $P$ and
$L$ are differential expressions with respect to a variable $x$ and where
$[P,L]$ denotes the commutator of $P$ and $L$. The question of commuting
differential expressions has therefore experienced a revival after an extensive
treatment at the beginning of the 20th century. A few years ago F. Gesztesy
and I have found that under certain circumstances $[P,L]=0$ if and only if
$Ly=zy$ has only meromorphic solutions for all values of $z$. In this talk
this relationship will be reviewed and the most recent results in this direction
will be presented.
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