Journal of Mathematical Sciences

, Volume 83, Issue 1, pp 93–105 | Cite as

Inverse scattering transform method for the Zakharov-Manakov system

  • V. D. Lipovsky
  • A. V. Shirokov


The inverse scattering transform method for the dimensionally reduced self-dual equations of the Yang-Mills fields (Zakharov-Manakov system) is developed. Reductions on the scattering data are obtained. The resolvent theory for the auxiliary linear problem is developed. Dispersion relations and trace identities are presented. Bibliography: 4 titles.


Dispersion Relation Linear Problem Inverse Scattering Trace Identity Auxiliary Linear 


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Literature Cited

  1. 1.
    S. V. Manakov and V. E. Zakharov, “Three-dimensional model of relativistic-invariant field theory, integrable by the inverse scattering transform,”Lett. Math. Phys.,5, 247–253 (1981).CrossRefMathSciNetGoogle Scholar
  2. 2.
    Javier Villarroel, “Scattering data for the self-duality equations,”Inverse Problems,5, No. 6, 1157–1162 (1989).CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    A. S. Fokas and M. J. Ablowitz, “On the inverse scattering of the time dependent Schrödinger equation and the associated Kadomtsev-Petviashvili-I equation,”Stud. Appl. Math.,69, 211–228 (1983).MathSciNetGoogle Scholar
  4. 4.
    K. Pohlmeyer, “On the Lagrangian theory of anti-self-dual fields in four-dimensional Euclidian space,”Commun. Math. Phys.,72 37–47 (1980).CrossRefMathSciNetGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • V. D. Lipovsky
  • A. V. Shirokov

There are no affiliations available

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