KdV hierarchy via Abelian coverings and operator identities

  title={KdV hierarchy via Abelian coverings and operator identities},
  author={Benjamin Eichinger and Tom Vandenboom and Peter Yuditskii},
  journal={Transactions of the American Mathematical Society, Series B},
We establish precise spectral criteria for potential functions V V of reflectionless Schrödinger operators L V = − ∂ x 2 + V L_V = -\partial _x^2 + V to admit solutions to the Korteweg–de Vries (KdV) hierarchy with V 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… Expand

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