Skip to main content
SpringerLink
Log in

A camassa—Holm equation interacted with the degasperis—procesi equation

  • Published:
Czechoslovak Journal of Physics Aims and scope

Abstract

We present two different Hamiltonian extensions of the Degasperis-Procesi equation. The construction based on the observation that the second Hamiltonian operator of the Degasperis-Procesi equation could be considered as the Dirac reduced Poisson tensor of the second Hamiltonian operator of the Boussinesq equation. The first extension describes the interaction between Camassa-Holm and Degasperis-Procesi equation while the second gives us the two component generalization of the Degasperis-Procesi equation.

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. R. Camassa and D. Holm: Phys. Rev. Lett.71 (1993) 1661.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  2. R. Camassa, D. Holm, and J.M. Hyman: Advances in Applied Mechanics31 (1994) 1.

    Article  Google Scholar 

  3. A. Degasparis, A. Hone, and D. Holm: inNEEDS 2001 Proceedings; nlin.SI/0205023.

  4. A. Degasparis, A. Hone, and D. Holm: inProc. Nonlinear Physics II, Gallipoli 2002, World Scientific; nlin.SI/0209008.

  5. B. Fuchssteiner: Physica D95 (1996) 229.

    Article  MATH  MathSciNet  Google Scholar 

  6. A. Hone and J. Wang: Inverse Problems19 (2003) 129.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  7. A. Hone: J. Phys. A: Math. Gen.32 (1999) L307.

    Google Scholar 

  8. Z. Popowicz: nlin.SI/0604067.

  9. M. Chen, Si-Qi Liu, and Y. Zhang: nlin. SI/0501028.

  10. G. Falqui: J. Phys. A: Math. Gen39 (2006) 327.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  11. H. Aratyn, J.F. Gomes, and A.H. Zimerman: J. Phys. A: Math. Gen39 (2006) 1099.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  12. W. Oevel and O. Ragnisco: Physica A161 (1990) 181.

    Article  ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Theoretical Physics, University of Wrocław, pl. M. Borna 9, 50–205, Wrocław, Poland

    Ziemowit Popowicz

Authors
  1. Ziemowit Popowicz
    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

Popowicz, Z. A camassa—Holm equation interacted with the degasperis—procesi equation. Czech J Phys 56, 1263–1268 (2006). https://doi.org/10.1007/s10582-006-0435-5

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10582-006-0435-5

PACS

Key words

Search

Navigation