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Toda lattice with a special self-consistent source

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Abstract

We describe a method for integrating the Toda lattice with a self-consistent source using the inverse scattering method for a discrete Sturm-Liouville operator with moving eigenvalues.

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References

  1. M. J. Ablowitz, D. J. Kaup, A. C. Newell, and H. Segur, Stud. Appl. Math., 53, 249 (1974).

    MathSciNet  Google Scholar 

  2. A. C. Newell, “The inverse scattering transform,” in: Solitons (Topics Current Phys., Vol. 17, R. K. Bullough and P. J. Caudrey, eds.), Springer, Berlin (1980), p. 177.

    Google Scholar 

  3. F. Calogero and A. Degasperis, Spectral Transform and Solitons. (Stud. Math. Appl., Vol. 13), Vol. 1, Tools to Solve and Investigate Nonlinear Evolution Equations, North-Holland, Amsterdam (1982).

    Google Scholar 

  4. S. V. Manakov, Soviet Phys. JETP, 40, 269 (1974).

    ADS  MathSciNet  Google Scholar 

  5. H. Flaschka, Progr. Theoret. Phys., 51, 703 (1974).

    Article  MathSciNet  Google Scholar 

  6. Ag. Kh. Khanmamedov, Ukrainian Math. J., 57, 1350 (2005).

    Article  MathSciNet  Google Scholar 

  7. V. K. Mel’nikov, Inverse Problems, 6, 809 (1990).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  8. G. U. Urasboev and A. B. Khasanov, Theor. Math. Phys., 129, 1341 (2001).

    Article  MATH  Google Scholar 

  9. K. M. Case and M. Kac, J. Math. Phys., 14, 594 (1973).

    Article  ADS  MathSciNet  Google Scholar 

  10. G. Sh. Guseinov, Soviet Math. Dokl., 17, 1684 (1976).

    MATH  Google Scholar 

  11. M. Toda, Theory of Nonlinear Lattices (Springer Ser. Solid-State Sci., Vol. 20), Springer, Berlin (1981).

    MATH  Google Scholar 

  12. L. A. Takhtadzhan and L. D. Faddeev, The Hamiltonian Methods in the Theory of Solitons [in Russian], Nauka, Moscow (1986); English transl.: L. D. Faddeev and L. A. Takhtajan, Springer, Berlin (1987).

    Google Scholar 

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Correspondence to G. U. Urazboev.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 2, pp. 305–315, February, 2008.

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Urazboev, G.U. Toda lattice with a special self-consistent source. Theor Math Phys 154, 260–269 (2008). https://doi.org/10.1007/s11232-008-0025-8

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  • DOI: https://doi.org/10.1007/s11232-008-0025-8

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