Skip to main content
SpringerLink
Log in

Canonical structure of evolution equations with non-linear dispersive terms

  • Published:
Pramana Aims and scope Submit manuscript

Abstract

The inverse problem of the variational calculus for evolution equations characterized by non-linear dispersive terms is analysed with a view to clarify why such a system does not follow from Lagrangians. Conditions are derived under which one could construct similar equations which admit a Lagrangian representation. It is shown that the system of equations thus obtained can be Hamiltonized by making use of the Dirac’s theory of constraints. The specific results presented refer to the third- and fifth-order equations of the so-called distinguished subclass.

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. F Calogero and A Degesparis,Spectral transform and solitons (North Holland Publ. Co., NY, 1982) vol. 1

    MATH  Google Scholar 

  2. P Rosenau and J M Hyman,Phys. Rev. Lett. 70, 564 (1993)

    Article  MATH  ADS  Google Scholar 

  3. B Dey and A Khare,J. Phys. 33, 5335 (2000)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  4. S A Hojman and L C Shepley,J. Math. Phys. 32, 142 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  5. G Darboux, Ivieme partie (Gauthier-Villars Paris, 1891)

    Google Scholar 

  6. G Lopez,Ann. Phys. (NY) 251, 363 (1996)

    Article  MATH  ADS  Google Scholar 

  7. R M Santili,Foundations of theoretical mechanics (Springer-Verlag, NY, 1978) vol. 1

    Google Scholar 

  8. P J Olver,Applications of Lie groups to differential equations (Springer-Verlag, NY, 1993)

    MATH  Google Scholar 

  9. E C G Sudarshan and N Mukunda,Classical dynamics: A modern perspective (John-Wiley and Sons Inc., NY, 1974)

    MATH  Google Scholar 

  10. P J Olver,J. Math. Phys. 27, 2495 (1986)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  11. Y Nutku,J. Phys. A29, 3257 (1996)

    ADS  MathSciNet  Google Scholar 

  12. R M Santili,Foundations of theoretical mechanics (Springer-Verlag, NY, 1978) vol. II

    Google Scholar 

  13. P Rosenau,Phys. Lett. A230, 305 (1997)

    ADS  MathSciNet  Google Scholar 

  14. V G Karmanov,Mathematical programming (Mir Publishers, Moscow, 1989)

    MATH  Google Scholar 

  15. F J deUrries and J Julve,J. Phys. A31, 6949 (1998)

    ADS  MathSciNet  Google Scholar 

  16. G B Whitham,Proc. R. Soc. (London) Ser. A283, 238 (1965)

    Article  ADS  MathSciNet  Google Scholar 

  17. P A M Dirac,Lectures on quantum mechanics (Belfer Graduate School Monograph Series No. 2, Yeshiva University, NY, 1964)

    Google Scholar 

  18. V E Zakharov and L D Faddeev,Funct. Anal. Appl. 5, 18 (1971)

    Google Scholar 

  19. C S Gardner,J. Math. Phys. 12, 1548 (1971)

    Article  MATH  ADS  Google Scholar 

  20. L Faddeev and R Jackiw,Phys. Rev. Lett. 60, 1692 (1988)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  21. H Montani,Int. J. Mod. Phys. A8, 4319 (1993)

    ADS  MathSciNet  Google Scholar 

  22. M M Horta-Barreira and C Wotzasek,Phys. Rev. D45 1410 (1992)

    ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Visva-Bharati University, 731 235, Santiniketan, India

    B. Talukdar, J. Shamanna & S. Ghosh

Authors
  1. B. Talukdar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Shamanna
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Ghosh
    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

Talukdar, B., Shamanna, J. & Ghosh, S. Canonical structure of evolution equations with non-linear dispersive terms. Pramana - J Phys 61, 99–107 (2003). https://doi.org/10.1007/BF02704514

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02704514

Keywords

PACS Nos

Search

Navigation