Advertisement

Solitons pp 86-104 | Cite as

Gauge Unification of Integrable Nonlinear Systems

  • A. Kundu
Part of the Springer Series in Nonlinear Dynamics book series (SSNONLINEAR)

Abstract

Gauge equivalence of generalized NLS type equations is established with its possible application to find out soliton solutions and with the generation of new integrable systems. Through certain gauge choices some realistic models are exactly solved. Explicit auto BT for different classes of equations are also obtained by gauge transformation.

Keywords

Gauge Transformation Soliton Solution Noncompact Manifold Backlund Transform Gauge Equivalent 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    C.S. Gardner, J. M. Greene, M. D. Kruskal and R. M. Miura, Phys. Rev. Lett. 19 (1967) 1095.ADSMATHCrossRefGoogle Scholar
  2. [2]
    V. I. Zakharov and A. B. Shabat, Zh Eksp. Theor. Fiz. 61 (1971)118.Google Scholar
  3. [3]
    M. J. Ablowitz, D. J. Kaup, A. C. Newell and H. Segur, Stud. Appl. Math. 53 (1974) 249.MathSciNetGoogle Scholar
  4. [4a]
    A. Kundu, Lett. Math. Phys. 6 (1982) 479.MathSciNetADSMATHCrossRefGoogle Scholar
  5. [4b]
    A. Kundu and O. Pashaev, J. Phys. C16 (1983) L585.ADSGoogle Scholar
  6. [5]
    A. Kundu, J. Math. Phys. 25 (1984) 3493.MathSciNetCrossRefGoogle Scholar
  7. [6]
    A. Kundu, J. Phys. A19 (1986) 1303.MathSciNetADSGoogle Scholar
  8. [7]
    A. Kundu, J. Phys. A (1986) (in press).Google Scholar
  9. [8]
    A. Kundu, Physica D (1986) (in press).Google Scholar
  10. [9]
    M. Lakshmanan, Phys. Lett. 61A (1977) 53.ADSGoogle Scholar
  11. [10]
    K. Pohlmayer, Comm. Math. Phys. 46 (1976) 207.MathSciNetADSCrossRefGoogle Scholar
  12. [11]
    V. I. Zakharov and L. A. Takhtajan, Teor. Math. Fiz. 38 (1979) 26.Google Scholar
  13. [12]
    H. Eichenherr and J. Honnerkamp, J. Math. Phys. 22 (1981) 374;MathSciNetADSMATHCrossRefGoogle Scholar
  14. [12]a
    J. Honnerkamp, J. Math. Phys. 22 (1981) 277.MathSciNetADSCrossRefGoogle Scholar
  15. [13]
    S. J. Orfanidis, Phys. Rev. D21 (1981) 1513.MathSciNetADSGoogle Scholar
  16. [14]
    R. Sasaki and Th. W. Ruijgrok, Physica 113A (1982) 388.MathSciNetADSGoogle Scholar
  17. [15]
    V. I. Zakharov and A. B. Shabat, Zh. Eksp. Teor. Fiz. 61 (1973)118.Google Scholar
  18. [16]
    V. Makhankov, Phys. Lett. 81A (1981) 156.MathSciNetADSGoogle Scholar
  19. [17]
    D. J. Kaup and A. C. Newell, J. Math. Phys. 19 (1978) 798.MathSciNetADSMATHCrossRefGoogle Scholar
  20. [18]
    M. Wadati, K. Konno and Y. H. Ichikawa, J. Phys. Soc. Japan 46 (1979) 1965.MathSciNetADSCrossRefGoogle Scholar
  21. [19]
    H. H. Chen, Y. C. Lee and C. S. Liu, Phys. Scr. 20 (1979) 490.MathSciNetADSMATHCrossRefGoogle Scholar
  22. [20]
    M. Wadati, K. Konno and Y. H. Ichikawa, J. Phys. Soc. Japan 47 (1979) 1698.MathSciNetADSCrossRefGoogle Scholar
  23. [21]
    V. S. Gerdzikov and M. I. Ivanov, Preprint E2–82–959 JINR, Dubna (1982).Google Scholar
  24. [22]
    R. S. Johnson, Proc. Roy. Soc. Lond. A357 (1977) 131.ADSGoogle Scholar
  25. [23]
    A. C. Newell, SIAM J. Appl. Math. 35 (1978) 650.MathSciNetMATHCrossRefGoogle Scholar
  26. [24]
    D. J. Benney, Stud. Appl. Math. 56 (1977) 81.Google Scholar
  27. [25]
    M. Boiti, F. Pempinelli and G. Z. Tu, Prog. Theor. Phys. 69 (1983) 48.MathSciNetADSMATHCrossRefGoogle Scholar
  28. [26]
    L. A. Takhtajan, Phys. Lett. 64A (1977) 235.MathSciNetADSGoogle Scholar
  29. [27]
    A. V. Mikhailov and A. B. Shabat, Phys. Lett. 116A (1986) 191.MathSciNetADSGoogle Scholar
  30. [28]
    R. Dodd and A. Fordy, Dublin Inst, preprint D/AS-STP 82–08(1982).Google Scholar
  31. [29]
    R. M. Miura, ed., Bäcklund Transformations, Lecture Notes in Mathemathics, No. 515 (Springer, Berlin, 1976).MATHGoogle Scholar
  32. [30]
    M. Wadati and K. Sogo, J. Phys. Soc. Japan 52 (1983) 394.MathSciNetADSCrossRefGoogle Scholar
  33. [31]
    N. N. Bogolyubov, A. K. Prikarpatskii, A. M. Kurbatov and V. G. Samolienko, TMF 65 (1985) 271.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • A. Kundu
    • 1
  1. 1.Theoretical Nuclear Physics DivisionSaha Institute of Nuclear PhysicsCalcuttaIndia

Personalised recommendations