Skip to main content
SpringerLink
Log in

Reciprocal transformations for a spectral problem in 2+1 dimensions

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

Abstract

We present two reciprocal transformations for a spectral problem in 2+1 dimensions. Reductions of the transformed equations to 1+1 dimensions include the Degasperis-Procesi and Vakhnenko-Parkes equations.

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. P. G. Estévez and S. L. Leble, Inverse Problems, 11, 925–937 (1995).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  2. P. G. Estévez and J. Prada, J. Nonlinear Math. Phys., 12(Suppl. 1), 266–279 (2005).

    Article  MathSciNet  Google Scholar 

  3. P. G. Estévez, M. L. Gandarias, and J. Prada, Phys. Lett. A, 343, 40–47 (2005).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  4. J. Weiss, J. Math. Phys., 24, 1405–1413 (1983).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  5. P. G. Estévez and J. Prada, J. Phys. A, 38, 1287–1297 (2005).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  6. S. Abenda and T. Grava, J. Phys. A, 40, 10769–10790 (2007).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  7. A. Degasperis, D. D. Holm, and A. N. W. Hone, Theor. Math. Phys., 133, 1463–1474 (2002).

    Article  MathSciNet  Google Scholar 

  8. C. Rogers and M. C. Nucci, Phys. Scripta, 33, 289–292 (1986).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  9. N. Euler, M. L. Gandarias, M. Euler, and O. Lindblom, J. Math. Anal. Appl., 257, 21–28 (2001).

    Article  MATH  MathSciNet  Google Scholar 

  10. P. G. Estévez and J. Prada, J. Nonlinear Math. Phys., 11, 164–179 (2004).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  11. V. O. Vakhnenko, J. Phys. A, 25, 4181–4187 (1992).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  12. A. Hone and J. P. Wang, Inverse Problems, 19, 129–145 (2003).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  13. V. O. Vakhnenko and E. J. Parkes, “The connection of the Degasperis-Procesi equation with the Vakhnenko equation,” in: Symmetry in Nonlinear Mathematical Physics (Part 1, Proc. Inst. Mat. Nats. Akad. Nauk Ukr. Mat. Zastos., Vol. 50, A. G. Nikitin, V. M. Boyko, R. O. Popovych, and I. A. Yehorchenko, eds.), Natsīonal. Akad. Nauk Ukraïni Īnst. Mat., Kiev (2004), pp. 493–497.

    Google Scholar 

  14. V. O. Vakhnenko, E. J. Parkes, and A. J. Morrison, Chaos Solitons Fractals, 17, 683–692 (2003).

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Facultad de Ciencias, Universidad de Salamanca, Salamanca, Spain

    P. G. Estévez

Authors
  1. P. G. Estévez
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to P. G. Estévez.

Additional information

Prepared from an English manuscript submitted by the author; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 159, No. 3, pp. 411–417, June, 2009.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Estévez, P.G. Reciprocal transformations for a spectral problem in 2+1 dimensions. Theor Math Phys 159, 763–769 (2009). https://doi.org/10.1007/s11232-009-0064-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11232-009-0064-9

Keywords

Search

Navigation