Skip to main content
SpringerLink
Log in

Periodic Toda chain with an integral source

  • Published:
Theoretical and Mathematical Physics Aims and scope Submit manuscript

Abstract

We use the inverse spectral transform method to integrate the periodic Toda chain with an integral source.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. Toda, Progr. Theoret. Phys. Suppl., 45, 174–200 (1970).

    Article  ADS  Google Scholar 

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

    Book  MATH  Google Scholar 

  3. S. V. Manakov, Soviet Phys. JETP, 1975, 269–274.

    Google Scholar 

  4. H. Flaschka, Progr. Theoret. Phys., 51, 703–716 (1974).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  5. B. A. Dubrovin, V. B. Matveev, and S. P. Novikov, Russ. Math. Surveys, 31, 59–146 (1976).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  6. E. Date and S. Tanaka, Progr. Theoret. Phys., 55, 217–222 (1976).

    Article  MathSciNet  Google Scholar 

  7. I. M. Krichever, Russ. Math. Surveys, 33, 255–256 (1978).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  8. V. G. Samoilenko and A. K. Prikarpatskii, Ukrainian Math. J., 34, 380–385 (1982).

    Article  MathSciNet  Google Scholar 

  9. M. J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform (SIAM Stud. Appl. Math., Vol. 4), SIAM, Philadelphia (1981).

    Book  MATH  Google Scholar 

  10. V. K. Mel’nikov, Phys. Lett. A, 128, 488–492 (1988).

    Article  MathSciNet  ADS  Google Scholar 

  11. G. Teschl, Jacobi Operators and Completely Integrable Lattices (Math. Surv. Monogr., Vol. 72), Amer. Math. Soc., Providence, R. I. (2000).

    MATH  Google Scholar 

  12. G. U. Urazboev, Theor. Math. Phys., 154, 260–269 (2008).

    Article  MATH  MathSciNet  Google Scholar 

  13. A. Cabada and G. U. Urazboev, Inverse Problems, 26, 085004 (2010).

    Article  MathSciNet  ADS  Google Scholar 

  14. X. Liu and Y. Zeng, J. Phys. A: Math. Gen., 38, 8951–8965 (2005).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  15. P. G. Grinevich and I. A. Taimanov, “Spectral conservation laws for periodic nonlinear equations of the Melnikov type,” in: Geometry, Topology, and Mathematical Physics (Amer. Math. Soc. Transl. Ser. 2, Vol. 224, V. M. Buchstaber and I. M. Krichever, eds.), Amer. Math. Soc., Providence, R. I. (2008), pp. 125–138.

    Google Scholar 

  16. A. B. Khasanov and A. B. Yakhshimuratov, Theor. Math. Phys., 164, 1008–1015 (2010).

    Article  MATH  Google Scholar 

  17. B. A. Babajanov, M. Fečkan, and G. U. Urazbaev, Commun. Nonlinear Sci. Numer. Simul., 22, 1223–1234 (2015).

    Article  MathSciNet  ADS  Google Scholar 

  18. H. Hochstadt, Linear Algebra Appl., 11, 41–52 (1975).

    Article  MATH  MathSciNet  Google Scholar 

  19. A. Hurwitz and R. Courant, Vorlesungen über allgemeine Funktionentheorie und elliptische Funktionen, Springer, Berlin (1964).

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Urgench State University, Urgench, Uzbekistan

    B. A. Babajanov & A. B. Khasanov

Authors
  1. B. A. Babajanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. B. Khasanov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to B. A. Babajanov.

Additional information

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 184, No. 2, pp. 253–268, August, 2015.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Babajanov, B.A., Khasanov, A.B. Periodic Toda chain with an integral source. Theor Math Phys 184, 1114–1128 (2015). https://doi.org/10.1007/s11232-015-0321-z

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11232-015-0321-z

Keywords

Search

Navigation