SpringerLink
Log in

Solutons of a nonisospectral and variable coefficient Korteweg-de Vries equation

  • Published:
Letters in Mathematical Physics Aims and scope Submit manuscript

Abstract

A new type of KdV equation with a nonisospectral Lax pair as well as variable coefficients is introduced. Its Lax pair is shown to be invariant under the Crum transformation. This leads to a Bäcklund transformation for the KdV equation and, hence, a method for solutions via an associated nonisospectral variable coefficient MKdV equation. Three generations of solutions are given. The 1-soliton solution shares the novel phenomenology associated with the boomeron, trappon, and zoomeron of Calogero and Degasperis.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Germany)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. AblowitzM. J. and SegurH., Solitons and Inverse Scattering Transform, SIAM, Philadelphia, 1981.

    Google Scholar 

  2. ChernS. S. and PengC. K., Lie groups and KdV equations, Manuscripta Math. 28, 207–217 (1979).

    Google Scholar 

  3. GuChaohao and HuHesheng, A unified explicit form of Bäcklund transformations for generalized hierarchies of KdV equations, Lett. Math. Phys. 11, 325–335 (1986).

    Google Scholar 

  4. LiY. S., The solution of soliton equation and Darboux transformation, in S. T.**ao and F. O.Pu (eds.), Proceedings: International Workshop on Applied Differential Equation, Bei**g 1985, World Scientific, Singapore, 1986.

    Google Scholar 

  5. NirmalaN., VedanM. J., and BabyB. V., Math. Phys. 27, 2640 (1986).

    Article  Google Scholar 

  6. NirmalaN., VedanM. J., and BabyB. V., Math. Phys. 27, 2644 (1986).

    Article  Google Scholar 

  7. LiYi-shen and BabyB. V., Variable Coefficient Korteweg-de Vries Equation: Darboux's Transformation, Exact Solutions and Conservation Laws, International Centre for Theoretical Physics, Miramare-Trieste, 1986.

    Google Scholar 

  8. CrumM. M., Associated Sturm-Liouville systems, Quart. J. Math. Oxford (2), 6, 121–127 (1955).

    Google Scholar 

  9. JohnsonR. S., J. Fluid Mech. 97, 701 (1980).

    Google Scholar 

  10. CalogeroF. and DegasperisA., Spectral Transform and Solitons I, Studies in Mathematics and its Application, Vol. 13, North-Holland, Amsterdam (1982).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Science Centre, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong

    W. L. Chan & Zheng Yu-Kun

Authors
  1. W. L. Chan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zheng Yu-Kun
    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

Chan, W.L., Yu-Kun, Z. Solutons of a nonisospectral and variable coefficient Korteweg-de Vries equation. Lett Math Phys 14, 293–301 (1987). https://doi.org/10.1007/BF00402138

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00402138

Keywords

Search

Navigation