Skip to main content
SpringerLink
Log in

On the Prolongation of a Hierarchy of Hydrodynamic Chains

  • Conference paper
New Trends in Integrability and Partial Solvability

Part of the book series: NATO Science Series ((NAII,volume 132))

Abstract

The prolongation of a hierarchy of hydrodynamic chains previously studied by the authors is presented and the properties of the differential reductions of the enlarged hierarchy are derived. Several associated nonlinear integrable models are exhibited. In particular, it is found that the Camassa-Holm equation can be described as a second-order differential reduction of one of the new flows included in the hierarchy.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. L. Martínez Alonso and A. B. Shabat, Phys.Lett. A 300, 58 (2002).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. L. Martínez Alonso and A. B. Shabat, J. Non. Math. Phys. 10, 229 (2003).

    Article  MATH  Google Scholar 

  3. V. G. Mikhalev, Funct. Anal. Appl. 26 No 2, 140 (1992).

    Article  MathSciNet  Google Scholar 

  4. M. Jaulent and I. Miodek, Lett. Math. Phys. 1, 243 (1976); Lett. Nuovo Cimento 20, 655 (1977).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. L. Martínez Alonso, J. Math. Phys. 21, 2342 (1980).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. M. Antonowicz and A. P. Fordy, Physica 28 D, 345 (1987).

    MathSciNet  MATH  Google Scholar 

  7. A. Shabat, Universal models of solitonic hierarchies. To appear in Theor. Math. Phys., June 2003.

    Google Scholar 

  8. A. N. W. Hone, Phys. Lett. A 249, 46 (1998).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. R. Heredero, V. Sokolov and A. B. Shabat, A new class of linearizable equations, to be published.

    Google Scholar 

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

    Article  MathSciNet  ADS  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Landau Institute for Theoretical Physics, RAS, Moscow, 117 334, Russia

    A. B. Shabat

  2. Departamento de Física Teórica II, Universidad Complutense, E28040, Madrid, Spain

    L. Martínez Alonso

Authors
  1. A. B. Shabat
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. Martínez Alonso
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Landau Institute for Theoretical Physics, Russian Academy of Science, Moscow, Russia

    A. B. Shabat

  2. Departamento de Física Teórica II, Universidad Complutense de Madrid, Spain

    A. González-López , M. Mañas , L. Martínez Alonso  & M. A. Rodríguez , ,  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer Science+Business Media Dordrecht

About this paper

Cite this paper

Shabat, A.B., Martínez Alonso, L. (2004). On the Prolongation of a Hierarchy of Hydrodynamic Chains. In: Shabat, A.B., González-López, A., Mañas, M., Martínez Alonso, L., Rodríguez, M.A. (eds) New Trends in Integrability and Partial Solvability. NATO Science Series, vol 132. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1023-8_10

Download citation

  • DOI: https://doi.org/10.1007/978-94-007-1023-8_10

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-1836-7

  • Online ISBN: 978-94-007-1023-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation