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On Some Solvable Classes of Nonlinear Nonisospectral Difference Equations

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We investigate different measure transformations of the mapping-multiplication type in the cases where the corresponding chains of differential equations can be efficiently found and integrated.

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REFERENCES

  1. N. I. Akhiezer, The Classical Moment Problem and Some Related Questions in Analysis [in Russian], Fizmatgiz, Moscow (1961); English translation: Hafner, New York (1965).

    Google Scholar 

  2. Yu. M. Berezans'kyi, Expansions in Eigenfunctions of Self-Adjoint Operators [in Russian], Naukova Dumka, Kiev (1965); English translation: American Mathematical Society, Providence (1968).

    Google Scholar 

  3. M. Toda, Theory of Nonlinear Lattices, Springer (1981).

  4. Yu. M. Berezans'kyi, “Integration of nonlinear difference equations by the inverse spectral problem method,” Sov. Math. Dokl., 21, 264–267 (1985).

    Google Scholar 

  5. Yu. M. Berezans'kyi, “The integration of semi-infinite Toda chain by means of inverse spectral problem,” Reports Math. Phys., 24, 21–47 (1986).

    Article  Google Scholar 

  6. J. Moser, “Three integrable Hamiltonian systems connected with isospectral deformations,” Adv. Math., 16, No.2, 197–220 (1975).

    Article  Google Scholar 

  7. M. Kac and P. van Moerbeke, “On an explicitly soluble system of nonlinear differential equations related to certain Toda lattices,” Adv. Math., 16, No.2, 160–169 (1975).

    Article  Google Scholar 

  8. Yu. M. Berezans'kyi and M. Shmoish, “Nonisospectral flows on semi-infinite Jacobi matrices,” Nonlin. Math. Phys., 1, 116–146 (1994).

    Google Scholar 

  9. Yu. M. Berezans'kyi, “Integration of nonlinear nonisospectral difference-differential equations by means of the inverse spectral problem,” in: Proceedings of the First Workshop on Nonlinear Physics (1995), pp. 11–20.

  10. F. Calogero and A. Degasperis, Spectral Transform and Solitons: Tools to Solve and Investigate Nonlinear Evolution Equations, North-Holland, Amsterdam (1982).

    Google Scholar 

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Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 3, pp. 356–365, March, 2005.

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Mokhon'ko, O.A. On Some Solvable Classes of Nonlinear Nonisospectral Difference Equations. Ukr Math J 57, 427–439 (2005). https://doi.org/10.1007/s11253-005-0200-0

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  • DOI: https://doi.org/10.1007/s11253-005-0200-0

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