Akhmetshin, A. A.; Volvovsky, Yu. S. The dynamics of zeros of finite-gap solutions of the Schrödinger equation. (English. Russian original) Zbl 1099.37053 Funct. Anal. Appl. 35, No. 4, 247-256 (2001); translation from Funkts. Anal. Prilozh. 35, No. 4, 8-19 (2001). Summary: 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. Cited in 1 Document MSC: 37K15 Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems 34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) 35J10 Schrödinger operator, Schrödinger equation 37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests 37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems PDFBibTeX XMLCite \textit{A. A. Akhmetshin} and \textit{Yu. S. Volvovsky}, Funct. Anal. Appl. 35, No. 4, 247--256 (2001; Zbl 1099.37053); translation from Funkts. Anal. Prilozh. 35, No. 4, 8--19 (2001) Full Text: DOI arXiv