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Nonlinear Science at the Dawn of the 21st Century pp 3–45Cite as

Nonlinear Coherent Phenomena in Continuous Media

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

Abstract

This review is devoted to description of coherent nonlinear phenomena in almost conservative media with applications to plasma physics, fluid dynamics and nonlinear optics. The main attention in the review is paid to consideration of solitons, collapses, and black holes. The latter is a quasi-stationary singular object which appear after the formation of a singularity in nonlinear wave systems. We discuss in details the qualitative reasons of the wave collapse and a difference between solitons and collapses, and apply to their analysis exact methods based on the integral estimates and the Hamiltonian formalism. These approaches are demonstrated mainly on the basic nonlinear models, i.e. on the nonlinear Schrödinger equation and the Kadomtsev-Petviashvili equation and their generalizations.

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Authors
  1. E.A. Kuznetsov
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  2. V.E. Zakharov
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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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Kuznetsov, E., Zakharov, V. (2000). Nonlinear Coherent Phenomena in Continuous Media. 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_1

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  • DOI: https://doi.org/10.1007/3-540-46629-0_1

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