Literature cited
Yu. M. Berezansky, “The integration of semiinfinite Toda chain by means of inverse spectral problem,” Preprint 84.79, Mat. Inst., Akad. Nauk Ukr. SSR, Kiev (1984).
Yu. M. Berezanskii, “Integration of nonlinear difference equations by the method of the inverse spectral problem,” Dokl. Akad. Nauk SSSR,28, No. 1, 16–19 (1985).
Yu. M. Berezanskii, “A remark on the loaded Toda chain,” Ukr. Mat. Zh.,37, No. 3, 352–355 (1985).
Yu. M. Berezanskii, Expansions in Eigenfunctions of Self-adjoint Operators, Am. Math. Soc. (1968).
M. Wadata, “Generalized matrix form of the inverse scattering method,” in: Solitons, R. K. Bullogh and P. J. Caudrey (eds.), Springer-Verlag, Berlin-Heidelberg-New York (1980).
F. V. Atkinson, Discrete and Continuous Boundary Problems, Academic Press, New York-London (1964).
A. M. Perelomov, “Integrable systems of classical mechanics and Lie algebras. Toda chains,” Preprint ITÉF-111, Inst. Theor. Exp. Phys., Acad. of Sci. of USSR, Moscow (1983).
J. Moser, “Finitely many mass points under the influence of an exponential potential,” in: Lect. Notes in Phys., Vol. 38, Springer-Verlag, Berlin (1975), pp. 97–122.
V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevskii, Soliton Theory: The Method of the Inverse Problem [in Russian], Nauka, Moscow (1980).
M. Toda, Theory of Nonlinear Lattices [Russian translation], Mir, Moscow (1984).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 38, No. 1, pp. 84–89, January–February, 1986.
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Berezanskii, Y.M., Gekhtman, M.I. & Shmoish, M.E. Integration of some chains of nonlinear difference equations by the method of the inverse spectral problem. Ukr Math J 38, 74–78 (1986). https://doi.org/10.1007/BF01056762
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DOI: https://doi.org/10.1007/BF01056762