Abstract
We study quasiperiodic (finite-gap) solutions of the Volterra chain satisfying an integrable boundary condition on the semiaxis. From the set of general finite-gap solutions, only those corresponding to the boundary-value problem are singled out, the relevant condition being expressed as a system of algebraic equations.
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R. F. Bikbaev and A. R. Its, “Algebro-geometric solutions of a boundary value problem for the nonlinear Schrödinger equation,” Mat. Zametki [Math. Notes], 45 (1989), no. 5, 3–9.
R. F. Bikbaev and V. O. Tarasov Algebra i Analiz [St. Petersburg Math. J.], 3 (1991), no. 4, 78–92.
V. É. Adler, I. T. Khabibulin, and A. B. Shabat, “A boundary-value problem for the KdV equation on the semiaxis,” Teoret. Mat. Fiz. [Theoret. and Math. Phys.], 110 (1997), no. 1, 98–113.
E. K. Sklyanin, “Boundary conditions for integrable equations,” Funktsional. Anal. i Prilozhen. [Functional Anal. Appl.], 21 (1987), no. 2, 86–87.
V. É. Adler and I. T. Khabibulin, “Boundary conditions for integrable chains,” Funktsional. Anal. i Prilozhen. [Functional Anal. Appl.], 31 (1997), no. 2, 1–14.
A. P. Veselov, “Integration of a stationary problem for the classical spin chain,” Teoret. Mat. Fiz. [Theoret. and Math. Phys.], 71 (1987), no. 1, 154–159.
J. Fay, Theta-Functions on Riemann Surface, Lecture Notes in Math., vol. 352, Springer-Verlag, New York, 1973.
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Translated from Matematicheskie Zametki, vol. 80, no. 5, 2006, pp. 696–700.
Original Russian Text Copyright © 2006 by V. L. Vereshchagin.
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Vereshchagin, V.L. Integrable boundary-value problem for the Volterra chain on the half-axis. Math Notes 80, 658–662 (2006). https://doi.org/10.1007/s11006-006-0186-4
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DOI: https://doi.org/10.1007/s11006-006-0186-4