Science in China Series A: Mathematics

, Volume 45, Issue 6, pp 706–715 | Cite as

Darboux transformation and solitons of Yang-Mills-Higgs equations in R2,1

  • Chaohao Gu


The Darboux transformations for soliton equations are applied to the Yang-Mills-Higgs equations. New solutions can be obtained from a known one via universal and purely algebraic formulas. SU(N) soliton solutions are constructed with explicit formulas. The interaction of solitons is described by the splitting theorem: each p-soliton is splitting into p single solitons asymptotically as t → ±∞.


Yang-Mills-Higgs equations Darboux transformations solitons splitting theorem 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Mason, L. J., Integrable and solvable systems, in Further Advances in Twistor Theory (eds. Mason, L. J., Hughston, L. P., Kobak, P. Z.), London: Longman Scientific Technical, 1995, 1–73.Google Scholar
  2. 2.
    Ward, R. S., Integrable systems and twistors, in Integrable Systems, Twistors, Loop Groups, and Riemann Surfaces (eds. Hitchin, N. J., Segal, G. B., Ward, R. S.), Oxford: Clarendon Press, 1999, 121–134.Google Scholar
  3. 3.
    Gu, C. H., Bäcklund transformations and Darboux transformations, in Soliton Theory and Its Applications (ed. Gu, C. H.), Springer-Verlag and Zhejiang Science and Technology Publishing House, 1995, 122–151.Google Scholar
  4. 4.
    Gu, C. H., Hu, H. S., Zhou, Z. X., Darboux Tranformation in Soliton Theory and Its Geometric Applications (in Chinese), Shanghai: Shanghai Scientific and Technical Publishers, 1999.Google Scholar
  5. 5.
    Gu, C. H., On the Darboux form of Bäcklund transformations, in Integrable Systems, Nankai Lectures on Math. Phys. (ed. Song, X. C.), Singapore: World Scientific, 1989, 162–168.Google Scholar
  6. 6.
    Matveev, V. B., Salle, M. A., Darboux Transformations and Solitons, Berlin: Springer-Verlag, 1991.MATHGoogle Scholar
  7. 7.
    Ustinov, N. V., The reduced self-dual Yang-Mills equation, binary and infinitesimal Darboux transformations, J. Math. Phys., 1998, 39: 976–985.MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Ward, R. S., Two integrable systems related to hyperbolic monopoles, Asian J. Math., 1999, 3: 325–332.MATHMathSciNetGoogle Scholar
  9. 9.
    Atiyah, M. F., Instantons in two and four dimensions, Commun. Math. Phys., 1984, 93: 437–451.MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Zhou, Z. X., Solutions of the Yang-Mills-Higgs equations in 2+1 dimensional anti-de Sitter space-time, J. Math. Phys., 2001, 42: 1085–1099.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Science in China Press 2002

Authors and Affiliations

  1. 1.Institute of MathematicsFudan UniversityShanghaiChina

Personalised recommendations