Spectral transform and nonlinear evolution equations

  • F. Calogero
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 98)


This is a terse introduction to the idea of the spectral transform method to solve nonlinear evolution equations.


Evolution Equation Spectral Problem Simple Setting Nonlinear Evolution Equation Nonlinear Partial Differential Equation 
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  1. 1.
    Besides the papers referred to in Degasperis'lecture notes, the following review papers are now available: F. Calogero, “Nonlinear evolution equations solvable by the inverse spectral transform”, in Mathematical Problems in Theoretical Physics, edited by G.F. Dell'Antonio, S.Doplicher and G.Jona-Lasinio, Lecture Notes in Physics 80, Springer, 1978; F.Calogero and A.Degasperis, “Nonlinear evolution equations solvable by the inverse spectral transform associated to the matrix Schrödinger equation” in Solitons, edited by R.K.Bullough and P. J. Caudrey, Lecture Notes in Physics, Springer, 1979; A.Degasperis, “Solitons, Boomerons and Trappons”, in Nonlinear Evolution Equations solvable by the Spectral Transform, Proceedings of a Symposium held at the Accademia dei Lincei in Rome June 1977), edited by F. Calogero, Research Notes in Mathematics 26, Pitman, 1978; F. Calogero and A. Degasperis, “The Spectral Transform: a Tool to Solve and Investigate Nonlinear Evolution Equations”, in Applied Inverse Problems, edited by P.C. Sabatier, Lecture Notes in Physics 85, Springer, 1978.Google Scholar
  2. 2.
    F. Calogero and A. Degasperis: “Inverse spectral problem for the one-dimensional Schrödinger equation with an additional linear potential”, “Solution by the spectral transform method of a nonlinear evolution equation including as a special case the cylindrical KdV equation”, “Conservation laws for a nonlinear evolution equation that includes as a special case the cylindrical KdV equation”, Lett. Nuovo Cimento 23, 143, 150, 155 (1978).Google Scholar
  3. 3.
    See, for instance: M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions, Dover, New York, 1965, chapter 10.Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • F. Calogero
    • 1
    • 2
  1. 1.Istituto di FisicaUniversita di RomaRomaItaly
  2. 2.Istituto Nazionale di Fisica NucleareSezione di RomaItaly

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