publication . Other literature type . Preprint . Article . 2019

KdV hierarchy via Abelian coverings and operator identities

B. Eichinger; T. VandenBoom; P. Yuditskii;
  • Published: 02 Jan 2019
  • Publisher: American Mathematical Society (AMS)
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.
arXiv: Nonlinear Sciences::Exactly Solvable and Integrable SystemsMathematics::Analysis of PDEsNonlinear Sciences::Pattern Formation and SolitonsMathematics::Spectral Theory
free text keywords: Mathematics - Spectral Theory, Mathematical Physics, 37K10, 37K15, 35Q53, 34L40, Pure mathematics, KdV hierarchy, Bitwise operation, Abelian group, Mathematics
Funded by
FWF| Extremal polynomials on subsets of the unit circle
  • Funder: Austrian Science Fund (FWF) (FWF)
  • Project Code: J 4138
  • Funding stream: Schrödinger-Programm
FWF| Spectral theory, abelian coverings and Iterations
  • Funder: Austrian Science Fund (FWF) (FWF)
  • Project Code: P 29363
  • Funding stream: Einzelprojekte
NSF| RTG: Analysis, Geometry, and Topology at Rice University
  • Funder: National Science Foundation (NSF)
  • Project Code: 1148609
  • Funding stream: Directorate for Mathematical & Physical Sciences | Division of Mathematical Sciences

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