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

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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.

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Authors and Affiliations

  1. Landau Institute for Theoretical Physics, Columbia University, USA

    A. A. Akhmetshin

  2. Landau Institute for Theoretical Physics, Columbia University, USA

    Yu. S. Volvovsky

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  1. A. A. Akhmetshin
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  2. Yu. S. Volvovsky
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Akhmetshin, A.A., Volvovsky, Y.S. The Dynamics of Zeros of Finite-Gap Solutions of the Schrödinger Equation. Functional Analysis and Its Applications 35, 247–256 (2001). https://doi.org/10.1023/A:1013118305726

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