Skip to main content

Symmetries and Recursions For N = 2 Supersymmetric KDV-Equation

  • Chapter
Integrable Hierarchies and Modern Physical Theories

Part of the book series: NATO Science Series ((NAII,volume 18))

  • 225 Accesses

Abstract

The N = 2 supersymmetric extension of KdV-equation is discussed. For the most intriguing case N = 2, a = 1, hierarchies of conservation laws, even and odd symmetries are constructed.Moreover the recursion on the odd hierarchies is given.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
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. P. Labelle and P. Mathieu, A new N = 2 supersymmetric Korteweg-de Vries equation, J.Math.Phys., 32(4):923–927, 1991.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. G.H.M. Roelofs, prolongation structures of Supersymmetric Systems, Ph.D. Thesis, Department of Applied Mathematics, University of Twente, Enschede, the Netherlands, 1993.

    Google Scholar 

  3. Z. Popowicz, The Lax formulaton of the “new “ N = 2 SUSY KdV equation, Phys.Lett. A, 174(5-6):411–415, 1993.

    Article  MathSciNet  ADS  Google Scholar 

  4. P.H.M. Kersten, Higher order supersymmetries and fermionic conservation laws of the supersymmetric extension of the KdV equation, Phys.Lett. A, 134(1):25–30, 1988.

    Article  MathSciNet  ADS  Google Scholar 

  5. I.S. Krasil’shchik, Complete Integrability of nonlinear PDE and Supersymmetry, Proceedings: Lie Groups, Geometric Structures and Differential Equations-One Hundred Years after Sophus Lie-RIMS Kokyuroku 1150, Kyoto University, Kyoto, Japan, 2000 (pp.147–152)

    Google Scholar 

  6. Kersten, Paul.H.M.; Supersymmetries and Recursion Operators for N=2 supersymmetric KdV-equation Proceedings: Lie Groups, Geometric Structures and Differential Equations-One Hundred Years after Sophus Lie-RIMS Kokyuroku 1150, Kyoto University, Kyoto, Japan, 2000 (pp.153–161)

    Google Scholar 

  7. I.S. Krasil’shchik and P.H.M. Kersten, Symmetries and Recursion Operators for Classical and Supersymmetric differential Equations, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2000.

    Google Scholar 

  8. P.H.M. Kersten and I.S. Krasil’shchik, Complete Integrability of a coupled KdV-MKdV Sytem, Advanced Studies in Pure Mathematics, Mathematical Society of Japan, to appear, 2001

    Google Scholar 

  9. S. Krivonos, A. Sorin. Extended N = 2 supersymmetric matrix (1, s)-KdV hierarchies. Phys. Lett. A251 (1999) 109.

    MathSciNet  ADS  Google Scholar 

  10. P. Mathieu. Open problems for the super KdV equation. AARMS-CRM Workshop on Baecklund and Darboux transformations. The Geometry of Soliton Theory. June 4-9, 1999. Halifax, Nova Scotia.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Kersten, P.H.M. (2001). Symmetries and Recursions For N = 2 Supersymmetric KDV-Equation. In: Aratyn, H., Sorin, A.S. (eds) Integrable Hierarchies and Modern Physical Theories. NATO Science Series, vol 18. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0720-7_11

Download citation

  • DOI: https://doi.org/10.1007/978-94-010-0720-7_11

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-0-7923-6963-9

  • Online ISBN: 978-94-010-0720-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics