Geodesic
Integrable boundary-value problem for the Volterra chain on the half-axis
Matematičeskie zametki, Tome 80 (2006) no. 5, pp. 696-700 
V. L. Vereshchagin. Integrable boundary-value problem for the Volterra chain on the half-axis. Matematičeskie zametki, Tome 80 (2006) no. 5, pp. 696-700. http://geodesic.mathdoc.fr/item/MZM_2006_80_5_a4/
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     title = {Integrable boundary-value problem for the {Volterra} chain on the half-axis},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] R. F. Bikbaev, A. R. Its, “Algebrogeometricheskie resheniya kraevoi zadachi dlya nelineinogo uravneniya Shrëdingera”, Matem. zametki, 45:5 (1989), 3–9 | MR | Zbl

[2] R. F. Bikbaev, V. O. Tarasov, “Neodnorodnaya kraevaya zadacha na poluosi i na otrezke dlya uravneniya Sine-Gordon”, Algebra i analiz, 3:4 (1991), 78–92 | MR | Zbl

[3] V. E. Adler, I. T. Khabibullin, A. B. Shabat, “Kraevaya zadacha dlya uravneniya KdF na poluosi”, TMF, 110:1 (1997), 98–113 | MR | Zbl

[4] E. K. Sklyanin, “Granichnye usloviya dlya integriruemykh uravnenii”, Funktsion. analiz i ego prilozh., 21:2 (1987), 86–87 | MR | Zbl

[5] V. E. Adler, I. T. Khabibullin, “Granichnye usloviya dlya integriruemykh tsepochek”, Funktsion. analiz i ego prilozh., 31:2 (1997), 1–14 | MR | Zbl

[6] A. P. Veselov, “Integrirovanie statsionarnoi zadachi dlya klassicheskoi spinovoi tsepochki”, TMF, 71:1 (1987), 154–159 | MR

[7] J. Fay, Theta-Functions on Riemann Surface, Lecture Notes in Math., 352, Springer-Verlag, New York, 1973 | MR | Zbl