Skip to main content
SpringerLink
Log in

Tzitzéica Equation and Proliferation of Nonlinear Integrable Equations

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

Abstract

The dressing method for the Tzitzéica equation is discussed. A modified Tzitzéica equation is derived using the proliferation procedure.

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. E. Schrödinger, Proc. Roy. Irish. Acad. A, 45 (1940).

  2. H. S. Green, Matrix Mechanics, Nordhoff, Groningen (1965).

    Google Scholar 

  3. A. P. Veselov and A. B. Shabat, Funct. Anal. Appl., 27, No. 2, 81 (1993).

    Google Scholar 

  4. A. B. Borisov and S. A. Zykov, Theor. Math. Phys., 115, 530 (1998).

    Google Scholar 

  5. R. Conte and M. Musette, J. Math. Phys., 40, 2092 (1999).

    Google Scholar 

  6. G. Tzitzéica, C. R. Acad. Sci. Paris, 144, 1257 (1907).

    Google Scholar 

  7. R. K. Dodd and R. K. Bullough, Proc. Roy. Soc. London. A, 351, 499 (1976).

    Google Scholar 

  8. A. V. Zhiber and A. B. Shabat, Dokl. Akad. Nauk SSSR, 247, 1103 (1979).

    Google Scholar 

  9. A. V. Mikhailov, JETP Letters, 30, 414 (1979).

    Google Scholar 

  10. V. E. Zakharov and A. B. Shabat, Funct. Anal. Appl., 13, 166 (1980); S. P. Novikov, S. V. Manakov, L. P. Pitaevsky, and V. E. Zakharov, Theory of Solitons: The Inverse Scattering Method [in Russian], Nauka, Moscow (1980); English transl., Plenum, New York (1984).

    Google Scholar 

  11. A. P. Fordy and J. Gibbons, J. Math. Phys., 21, 2508 (1981).

    Google Scholar 

  12. V. B. Matveev and M. A Salle, Darboux Transformation and Solitons, Springer, Berlin (1991).

    Google Scholar 

  13. S. S. Safin and R. A. Sharipov, Theor. Math. Phys., 95, 462 (1993).

    Google Scholar 

  14. A. V. Yurov, Theor. Math. Phys., 119, 731 (1999).

    Google Scholar 

  15. C. S. Gardner, J. M. Green, M. D. Kruskal, and R. M. Miura, Phys. Rev. Lett., 19, 1095 (1967).

    Google Scholar 

  16. A. B. Borisov, M. V. Pavlov, and S. A. Zykov, Physica D, 151-152, 104 (2001).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Ural Branch, Institute for the Physics of Metals, RAS, Ekaterinburg, Russia

    A. B. Borisov & S. A. Zykov

  2. Moscow State Aviation Technical University, Moscow, Russia

    M. V. Pavlov

Authors
  1. A. B. Borisov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. A. Zykov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. V. Pavlov
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Borisov, A.B., Zykov, S.A. & Pavlov, M.V. Tzitzéica Equation and Proliferation of Nonlinear Integrable Equations. Theoretical and Mathematical Physics 131, 550–557 (2002). https://doi.org/10.1023/A:1015162021255

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1015162021255

Keywords

Search

Navigation