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The long-time behaviour for perturbed wave-equations and related problems

  • Session II: Nonlinear waves — Solitons
  • Conference paper
  • First Online:
Trends in Applications of Pure Mathematics to Mechanics

Part of the book series: Lecture Notes in Physics ((LNP,volume 249))

This contribution to the proceedings contains chapters 1,2 and 3. The complete version of the paper appeared as a Preprint of the Mathematical Institute at Utrecht

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References

  • T.B.Benjamin, J.L.Bona, J.J.Mahony. Model equations for long waves in nonlinear dispersive systems. Phil.Trans. Roy. Soc. London A.272 (1972)

    Google Scholar 

  • J.L.Bona, W.G.Pritohard, L.R.Scott. A comparison of solutions of two model equations for long waves. Lectures in Applied Mathematics AM$ Vol.20 (1983)

    Google Scholar 

  • J.D.Cole. Perturbation methods in applied mathematics. Ginn — Blaisdell (1968)

    Google Scholar 

  • D.David, D.Levi, P.Winternitz. Solitons in straits of varying width and depth. Université de Montréal, Centre de Recherches Mathematique Preprint (1985)

    Google Scholar 

  • R.K.Dodd, J.C.Eilbeek, J.D.Gibbon, H.C.Morris. Solitons and nonlinear wave equations. Academic Press (1982)

    Google Scholar 

  • W.Eckhaus, A.van Harten. The inverse scattering transformation and the theory of solitons. North-Holland (1981)

    Google Scholar 

  • C.L. Franzen, J. Kevorkian. Uncoupled nonlinear evolution equations by multiple scale and reductive perturbation methods. Applied Math.Program, University of Washington, Seattle. Preprint (1984)

    Google Scholar 

  • R.GeeZ. Singular perturbations of hyperbolic type. Mathematical Center Amsterdam Troef (1978)

    Google Scholar 

  • B.B.Kadomtsev, V.I.Petviashvili. The stability of solitary waves in weakly dispersive media. Dokl.Akad. Nauk SSR 192 (1970)

    Google Scholar 

  • J.Kevorkian, J.D.Cole. Perturbation methods in applied mathematics. Sprineer (1981)

    Google Scholar 

  • F.de Kerf. Perturbation theory for the Korteweg-de Vries equation. Preprint Mathematical Institute Utrecht (1985)

    Google Scholar 

  • G.L.Lamb, Ir. Elements of soliton theory. Wiley-Interscience (1980)

    Google Scholar 

  • R.E.Meyer. On the meaning of the Boussinesq and Korteweg-de Vries equations. Bull.Cal. Math.Soc. 71 (1979)

    Google Scholar 

  • S.Novikov, S.V.Manakov, L.P.Pitaerskii, Y.E.Zakharov. Theory of Solitons. English translation by Consultant Bureau New York (1984)

    Google Scholar 

  • G.B.Whitham. Linear and nonlinear waves. John Wiley (1974)

    Google Scholar 

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Authors and Affiliations

  1. Mathematisch Instituut Rijksuniversiteit Utrecht, Germany

    Wiktor Eckhaus

Authors
  1. Wiktor Eckhaus
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Ekkehart Kröner Klaus Kirchgässner

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© 1986 Springer-Verlag

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Eckhaus, W. (1986). The long-time behaviour for perturbed wave-equations and related problems. In: Kröner, E., Kirchgässner, K. (eds) Trends in Applications of Pure Mathematics to Mechanics. Lecture Notes in Physics, vol 249. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0016391

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  • DOI: https://doi.org/10.1007/BFb0016391

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16467-8

  • Online ISBN: 978-3-540-39803-5

  • eBook Packages: Springer Book Archive

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