Spectral transform approach to Bäcklund transformations

  • A. Degasperis
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 226)


Evolution Equation Nonlinear Evolution Equation mKdV Equation Backlund Transformation Commutativity Theorem 
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  1. [1]
    R.K. Bullough, P.J. Caudrey (editors), Solitons, Topics in Current Physics, 17, Springer, Berlin, 1980.Google Scholar
  2. [2]
    F. Calogero, A. Degasperis, Spectral Transform and Solitons, North-Holland, Amsterdam, Vol. I, 1982; Vol. II, in preparation.Google Scholar
  3. [3]
    R.K. Dodd, J.C. Eilbeck, J.D. Gibbon, H.C. Morris, Solitons and Nonlinear Waves, Academic Press, New York, 1982.Google Scholar
  4. [4]
    R.M. Miura (editor), Bäcklund Transformations, Lecture Notes in Mathematics 515, Springer, Berlin, 1976.Google Scholar
  5. [5]
    C. Rogers, W.F. Shadwick, Bäcklund Transformations and Their Applications, Academic Press, New York, 1982.Google Scholar
  6. [6]
    F.A.E. Pirani, D.C. Robinson, W.F. Shabwick, Local Jet-bundle Formulation of Bäcklund Transformations, Reidel, Dordrecht, 1979.Google Scholar
  7. [7]
    P.C. Sabatier, “Rational reflection coefficients in one dimensional inverse scattering and applications”, preprint PM/83/5, Montpellier, 1983.Google Scholar
  8. [8]
    M.J. Ablowith, H. Segur, Solitons and Inverse Scattering Transform. SIAM, Philadelphia, 1981.Google Scholar
  9. [9]
    M. Boiti, B.G. Konopelchenko, F. Pempinelli, “Bäcklund Transformations via Gauge Transformations in 2+1 Dimensions” Inverse Problems (to be published).Google Scholar
  10. [10]
    F. Calogero, A. Degasperis, “Elementary Bäcklund Trasformations, nonlinear superposition formulae and algebraic construction of solutions for the nonlinear evolution equations solvable by the Zakharov-Shabat spectral problem”, Physica D (to be published).Google Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • A. Degasperis
    • 1
    • 2
  1. 1.Dipartimento di FisicaUniversità di RomaRomaItaly
  2. 2.Sezione di RomaIstituto Nazionale di Fisica NucleareItaly

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