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Functional Analysis and Its Applications

, Volume 35, Issue 4, pp 247–256 | Cite as

The Dynamics of Zeros of Finite-Gap Solutions of the Schrödinger Equation

  • A. A. Akhmetshin
  • Yu. S. Volvovsky
Article
  • 47 Downloads

Abstract

We study a system of particles on a Riemann surface with a puncture. This system describes the behavior of zeros of finite-gap solutions of the Schrödinger equation corresponding to a degenerate hyperelliptic curve. We show that this system is Hamiltonian and integrable by constructing action-angle type coordinates.

Keywords

Functional Analysis Riemann Surface Hyperelliptic Curve 
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Copyright information

© Plenum Publishing Corporation 2001

Authors and Affiliations

  • A. A. Akhmetshin
    • 1
  • Yu. S. Volvovsky
    • 2
  1. 1.Landau Institute for Theoretical PhysicsColumbia UniversityUSA
  2. 2.Landau Institute for Theoretical PhysicsColumbia UniversityUSA

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