Advertisement

Il Nuovo Cimento B (1971-1996)

, Volume 111, Issue 12, pp 1495–1505 | Cite as

Resolvent approach to the ablowitz-ladik linear system

  • A. K. Pogrebkov
  • M. C. Prati
Article

Summary

The resolvent operator corresponding to the Ablowitz-Ladik linear system with a generic potential is determined. We present the properties of this operator and, using them, we introduce Jost solutions, different from the ones known in the literature.

PACS

02.30.Jr Partial differential equations 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Ablowitz M. J. andLadik J.,J. Math. Phys.,16 (1975) 598.MathSciNetADSCrossRefMATHGoogle Scholar
  2. [2]
    Ablowitz M. J. andLadik J.,J. Math. Phys.,17 (1976) 1011.MathSciNetADSCrossRefMATHGoogle Scholar
  3. [3]
    Ablowitz M. J. andSegur H.,Solitons and the Inverse Scattering Transform (SLAM, Philadelphia) 1981.CrossRefMATHGoogle Scholar
  4. [4]
    Boiti M., Leon J. andPempinelli F.,J. Math. Phys.,37 (1996) 2824.MathSciNetADSCrossRefMATHGoogle Scholar
  5. [5]
    Takhtajan L.,Integrable cellular automata and AKNS hierarchy, inProceedings of the Workshop on Symmetries and Integrability of Differential Equations, Esterel, Canada,1994, CRM Proceedings and Lecture Notes, Vol.9 (1996) 371.Google Scholar
  6. [6]
    Wolfram S.,Theory and Applications of Cellular Automata (World Scientific, Singapore) 1986.MATHGoogle Scholar
  7. [7]
    Park J., Steiglitz K. andThurston W.,Physica D,19 (1986) 423.MathSciNetADSCrossRefMATHGoogle Scholar
  8. [8]
    Boiti M., Pempinelli F., Pogrebkov A. andPolivanov M.,Theor. Math. Phys.,93 (1992) 1200.MathSciNetCrossRefGoogle Scholar
  9. [9]
    Boiti M., Pempinelli F. andPogrebkov A.,Theor. Math. Phys.,99 (1993) 511.MathSciNetCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica 1996

Authors and Affiliations

  • A. K. Pogrebkov
    • 1
  • M. C. Prati
    • 2
  1. 1.Steklov Mathematical InstituteMoscowRussia
  2. 2.Scuola Normale Superiore di PisaINFN, Sezione di PisaPisaItaly

Personalised recommendations