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Three Sources and Three Component Parts of the Concept of Dissipative Solitons

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Dissipative Solitons: From Optics to Biology and Medicine

Part of the book series: Lecture Notes in Physics ((LNP,volume 751))

Abstract

We explain the notion of dissipative solitons within a historical perspective. We show that the ideas of the theory of dissipative solitons emerge from several fields, including classical soliton theory, nonlinear dynamics, with its theory of bifurcations, and Prigogine’s concept of self-organization. A new notion, emerging from this three-part foundation, allows us to build the novel concept of the dissipative soliton. We also show that reductions to lower dimensional systems have to be done carefully and should always include a comparison of the results with numerical simulations of the original equations.

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Authors and Affiliations

  1. Optical Sciences Group, Research School of Physical Sciences and Engineering, Australian National University, Acton, ACT 0200, Australia

    N. Akhmediev & A. Ankiewicz

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  1. N. Akhmediev
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  2. A. Ankiewicz
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Akhmediev, N., Ankiewicz, A. (2008). Three Sources and Three Component Parts of the Concept of Dissipative Solitons. In: Dissipative Solitons: From Optics to Biology and Medicine. Lecture Notes in Physics, vol 751. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78217-9_1

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  • DOI: https://doi.org/10.1007/978-3-540-78217-9_1

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