Skip to main content
SpringerLink
Log in

Traveling-Wave Solutions of the Calogero-Degasperis-Fokas Equation in 2+1 Dimensions

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

Abstract

Soliton solutions are among the more interesting solutions of the (2+1)-dimensional integrable Calogero-Degasperis-Fokas (CDF) equation. We previously derived a complete group classiffication for the CDF equation in 2+1 dimensions. Using classical Lie symmetries, we now consider traveling-wave reductions with a variable velocity depending on an arbitrary function. The corresponding solutions of the (2+1)-dimensional equation involve up to three arbitrary smooth functions. The solutions consequently exhibit a rich variety of qualitative behaviors. Choosing the arbitrary functions appropriately, we exhibit solitary waves and bound states.

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. K. Toda and S. Yu, Rep. Math. Phys., 48, 255 (2001).

    Article  Google Scholar 

  2. F. Calogero and A. Degasperis, J. Math. Phys., 22, 23 (1981).

    Article  Google Scholar 

  3. A. S. Fokas, J. Math. Phys., 21, 1318 (1980).

    Article  Google Scholar 

  4. A. Nakamura and R. Hirota, J. Phys. Soc. Japan, 48, 1755 (1980).

    Article  Google Scholar 

  5. K. M. Tamizhmani and M. Lakshmanan, Phys. Lett. A, 90, 159 (1982).

    Article  Google Scholar 

  6. P. Rosenau, Phys. Lett. A, 211, 265 (1996).

    Article  Google Scholar 

  7. W. K. Schief and C. Rogers, Proc. Roy. Soc. London A, 455, 3163 (1999).

    Google Scholar 

  8. M. V. Pavlov, Phys. Lett. A, 243, 245 (1998).

    Article  Google Scholar 

  9. H.-H. Chen, Phys. Rev. Lett., 33, 925 (1974).

    Article  Google Scholar 

  10. K. Toda and S. Yu, J. Math. Phys., 41, 4747 (2000).

    Article  Google Scholar 

  11. D. David, N. Kamran, D. Levi, and P. Winternitz, J. Math. Phys., 27, 1225 (1986).

    Article  Google Scholar 

  12. D. Levi and P. Winternitz, Phys. Lett. A, 129, 165 (1988).

    Article  Google Scholar 

  13. M. Senthil Velan and M. Lakshmanan, J. Nonlinear Math. Phys., 5, 190 (1998).

    Google Scholar 

  14. J. Ramirez, M. S. Bruzon, C. Muriel, and M. L. Gandarias, J. Phys. A, 36, 1467 (2002).

    Google Scholar 

  15. E. L. Ince, Ordinary Differential Equations [in Russian], DNTVU, Kharkov (1939); English transl., Dover, New York (1956).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Matematicas, Universidad de Cadiz, PO Box 40, 11510, Puerto Real, Cadiz, Spain

    M. L. Gandarias & S. Saez

Authors
  1. M. L. Gandarias
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Saez
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

__________

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 144, No. 1, pp. 44–55, July, 2005.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gandarias, M.L., Saez, S. Traveling-Wave Solutions of the Calogero-Degasperis-Fokas Equation in 2+1 Dimensions. Theor Math Phys 144, 916–926 (2005). https://doi.org/10.1007/s11232-005-0118-6

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11232-005-0118-6

Keywords

Search

Navigation