We establish precise spectral criteria for potential functions V of reflectionless Schrödinger operators LV = −∂x2 + V to admit solutions to the Korteweg–de Vries (KdV) hierarchy with V as an initial value. More gener-ally, our methods extend the classical study of algebro-geometric solutions for the KdV hierarchy to noncompact Riemann surfaces by defining generalized Abelian integrals and analogues of the Baker-Akhiezer function on infinitely connected domains with a uniformly thick boundary satisfying a fractional moment condition.
|Number of pages||44|
|Journal||Transactions of the American Mathematical Society Series B|
|State||Published - 2019|
Bibliographical noteFunding Information:
Received by the editors March 13, 2018, and, in revised form, August 21, 2018. 2010 Mathematics Subject Classification. Primary 37K10, 37K15, 35Q53, 34L40. The first author was supported by the Austrian Science Fund FWF, project no. J 4138-N32. The second author was supported in part by NSF grant DMS-1148609. The third author was supported by the Austrian Science Fund FWF, project no. P 29363-N32.
© 2019 by the authors under.