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Perturbation Theories for Nonlinear Waves

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Nonlinear Science at the Dawn of the 21st Century

Part of the book series: Lecture Notes in Physics ((LNP,volume 542))

Abstract

Some ideas and theories developed since 1960s to describe nonlinear waves with slowly varying parameters (modulated waves)are outlined. These theories are associated with different versions of the asymptotic perturbation method. In this framework, both quasi-periodic and solitary waves (solitons)can be treated. A scheme for reduction of a quasihyperbolic system to one or more evolution equations is also presented. Some challenges for the theory are briefly discussed.

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Authors
  1. Lev Ostrovsky
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  2. Konstantin Gorshkov
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Editor information

Editors and Affiliations

  1. Department of Mathematical Modelling, The Technical University of Denmark, Building 321, 2800, Kgs. Lyngby, Denmark

    P. L. Christiansen , M. P. Sørensen  & A. C. Scott ,  & 

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Ostrovsky, L., Gorshkov, K. (2000). Perturbation Theories for Nonlinear Waves. In: Christiansen, P.L., Sørensen, M.P., Scott, A.C. (eds) Nonlinear Science at the Dawn of the 21st Century. Lecture Notes in Physics, vol 542. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46629-0_2

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  • DOI: https://doi.org/10.1007/3-540-46629-0_2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66918-0

  • Online ISBN: 978-3-540-46629-1

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