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KdV hierarchy via Abelian coverings and operator identities by Eichinger, Benjamin; VandenBoom, Tom; Yuditskii, Peter is a scholarly article available to read on EtoBox.

What is KdV hierarchy via Abelian coverings and operator identities about?

We establish precise spectral criteria for potential functions $V$ of reflectionless Schr\"odinger operators $L_V = -\partial_x^2 + V$ 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.

Author

Eichinger, Benjamin; VandenBoom, Tom; Yuditskii, Peter

Published

2018

Language

EN