Nonlinear evolution equations solvable by the inverse spectral transform

  • F. Calogero
Main Lectures
Part of the Lecture Notes in Physics book series (LNP, volume 80)


The main ideas and some recent results on (classical) solitons are tersely surveyed.


Spectral Problem Nonlinear Evolution Equation Nonlinear Partial Differential Equation Schroedinger Equation Discrete Eigenvalue 
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.


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    Recently there have been very interesting developments on this last topic: H.Airault, H.P.McKean and J.Moser, “Rational and Elliptic Solutions of the Korteweg-de Vries Equation and a Related Many-Bo dy Problem”, (NYU preprint, to be published); D.V.Choodnovsky and G.V.Choodnovsky, “Pole Expansion of Nonlinear Partial Differential Equations”, Nuovo Cimento B (in press); F.Calogero, “Motion of poles and zeros of special solutions of nonlinear and linear partial differential equations and related “solvable” many-body problems”, Nuovo Cimento B (in press).Google Scholar
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    F.Calogero, “Generalized Wronskian Relations, One-Dimensional Schroedinger Equation and Nonlinear Partial Differential Equations Solvable by the inverse Scattering Method”, Nuovo Cimento 31B, 229–249 (1976). See also the papers of Ref.[71.Google Scholar
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    F.Calogero and A.Degasperis, “Special Solution of Coupled Nonlinear Evolution Equations with Bumps that Behave as Interacting Particles”, Lett.Nuovo Cimento 19,525–533 (1977).Google Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

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

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