The Dynamics of Zeros of Finite-Gap Solutions of the Schrödinger Equation
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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.
KeywordsFunctional Analysis Riemann Surface Hyperelliptic Curve
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