KdV hierarchy via Abelian coverings and operator identities
Sprache des Vortragstitels:
Englisch
Original Tagungtitel:
Analysis Seminar 2018, June 8-10, Traunkirchen
Sprache des Tagungstitel:
Englisch
Original Kurzfassung:
We establish precise spectral criteria for potential functions V of reflectionless Schr\"odinger operators $L_V=-\partial^2_x+V(x)$ to admit solutions to the Korteweg de-Vries (KdV) hierarchy with V as an initial value. More generally, 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.
Joint work with Benjamin Eichinger and Tom VandenBoom.
Forschungs-