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Spectral Transform and Solitons

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Statics and Dynamics of Nonlinear Systems

Part of the book series: Springer Series in Solid-State Sciences ((SSSOL,volume 47))

Abstract

This is a terse introduction to the spectral transform technique to solve certain classes of nonlinear evolution equations, and to the properties of the solutions of these nonlinear PDEs.

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References

  1. F.Calogero and A.Degasperis: Spectral Transform and Solitons:Tools to Solve and Investigate Nonlinear Evolution Equations. North Holland, Amsterdam. Volume One, 1982

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  2. F.Calogero and A.Degasperis: Spectral Transform and Solitons:Tools to Solve and Investigate Nonlinear Evolution Equations Volume Two, 1984.

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  3. J.Scott-Russell, “Report on waves”, in: Report of the fourteenth meeting of the British association for the advancement of science. John Murray, London, 1845. pp. 311–390

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  4. D.J.Korteweg and G. de Vries: “On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves”, Phil. Mag. 39, 422–443 (1895)

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  5. N.J.Zabusky and M.D.Kruskal: “Interactions of solitons in a collisionless plasma and the recurrence of initial states”, Phys. Rev. Lett. 15, 240–243 (1965)

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  6. C.S.Gardner, J.M.Greene, M.D.Kruskal and R.M.Miura: “Method for solving the Korteweg-de Vries equation”, Phys. Rev. Lett. 19, 1095–1097 (1967)

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Author information

Authors and Affiliations

  1. Dipartimento di Fisica, Istituto Nazionale di Fisica Nucleare, Sezione di Roma, Università di Roma, I-00185, Roma, Italy

    F. Calogero

Authors
  1. F. Calogero
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Editor information

Editors and Affiliations

  1. Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria 16, I-20133, Milano, Italy

    Giorgio Benedek

  2. Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, D-7000, Stuttgart, Fed. Rep. of Germany

    Heinz Bilz  & Roland Zeyher  & 

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© 1983 Springer-Verlag Berlin Heidelberg

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Calogero, F. (1983). Spectral Transform and Solitons. In: Benedek, G., Bilz, H., Zeyher, R. (eds) Statics and Dynamics of Nonlinear Systems. Springer Series in Solid-State Sciences, vol 47. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82135-6_2

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  • DOI: https://doi.org/10.1007/978-3-642-82135-6_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-82137-0

  • Online ISBN: 978-3-642-82135-6

  • eBook Packages: Springer Book Archive

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