On the Darboux matrices of Bäcklund transformations for AKNS systems


The auto-Bäcklund property of the Darboux matrices for AKNS systems is proved. A quite general form of the theorem of permutability is obtained in a universal way.

This is a preview of subscription content, access via your institution.


  1. 1.

    Wedati, M., Sanuki, H., and Konno, K., ‘Relationships Among Inverse Method, Bäcklund Transformations and Infinite Number of Conservation Laws’, Prog. Theoret. Phys. 53, 418–436 (1975).

    Google Scholar 

  2. 2.

    Rogers, C. and Shadwick, W. R., Bäcklund Transformations and their Applications, Academic Press, New York, 1982.

    Google Scholar 

  3. 3.

    Li, Y. S., ‘Gauge Transformations, Bäcklund Transformation and Nonlinear Superposition Laws’, to appear in Adv. Math.

  4. 4.

    Tien, C., ‘Bäcklund Transformation of Nonlinear Evolution Equations’, Acta Math. Appl. Sinica (1986).

  5. 5.

    Gu, C. H. and Hu, H. S., ‘A Unified Explicit Form of Bäcklund Transformations for Generalized Hierarchies of KdV Equations’, Lett. Math. Phys. 11, 325–335 (1986).

    Google Scholar 

  6. 6.

    Gu, C. H., ‘On the Bäcklund Transformations for the Generalized Hierarchies of Compound MKdV-SG Equations’, Lett. Math. Phys. 12, 31–41 (1986).

    Google Scholar 

  7. 7.

    Zhou, M. R., ‘The Darboux Transformations for AKNS Eigenvalue Problems and Knap-Newell Eigenvalue Problems’, Preprint of Chinese Univ. of Science and Technology, 1985.

Download references

Author information



Additional information

The work is supported by the Science Fund of the Chinese Academy of Sciences.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Chaohao, G., Zixiang, Z. On the Darboux matrices of Bäcklund transformations for AKNS systems. Lett Math Phys 13, 179–187 (1987). https://doi.org/10.1007/BF00423444

Download citation


  • Statistical Physic
  • Group Theory
  • AKNS System