Geodesic
The Dynamics of Zeros of Finite-Gap Solutions of the Schr\"odinger Equation
Funkcionalʹnyj analiz i ego priloženiâ, Tome 35 (2001) no. 4, pp. 8-19

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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. 
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     author = {A. A. Akhmetshin and Yu. S. Vol'vovskii},
     title = {The {Dynamics} of {Zeros} of {Finite-Gap} {Solutions} of the {Schr\"odinger} {Equation}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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     publisher = {mathdoc},
     volume = {35},
     number = {4},
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A. A. Akhmetshin; Yu. S. Vol'vovskii. The Dynamics of Zeros of Finite-Gap Solutions of the Schr\"odinger Equation. Funkcionalʹnyj analiz i ego priloženiâ, Tome 35 (2001) no. 4, pp. 8-19. http://geodesic.mathdoc.fr/item/FAA_2001_35_4_a1/