Geodesic
On rational and periodic solutions of stationary KdV equations
Documenta mathematica, Tome 4 (1999), pp. 109-126.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Stationary solutions of higher order KdV equations play an important role for the study of the KdV equation itself. They give rise to the coefficients of the associated Lax pair $(P,L)$ for which $P$ and $L$ have an algebraic relationship (and are therefore called algebro-geometric). This paper gives a sufficient condition for rational and simply periodic functions which are bounded at infinity to be algebro-geometric as those potentials of $L$ for which $Ly=zy$ has only meromorphic solutions. It also gives a new elementary proof that this is a necessary condition for any meromorphic function to be algebro-geometric.
Classification : 35Q53, 34A20, 58F07
Keywords: KdV equation, algebro-geometric solutions of integrable systems, meromorphic solutions of linear differential equations 
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     author = {Weikard, R.},
     title = {On rational and periodic solutions of stationary {KdV} equations},
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Weikard, R. On rational and periodic solutions of stationary KdV equations. Documenta mathematica, Tome 4 (1999), pp. 109-126. http://geodesic.mathdoc.fr/item/DOCMA_1999__4__a16/