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General Theory of Solitons

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Soliton-driven Photonics

Part of the book series: NATO Science Series ((NAII,volume 31))

Abstract

A soliton is a concept which describes various physical phenomena ranging from solitary waves on a water surface to ultra-short optical pulses in an optical fiber. The main feature of solitons is that they can propagate long distances without visible changes. From a mathematical point of view, a soliton is a localized solution of a partial differential equation describing the evolution of a nonlinear system with an infinite number of degrees of freedom. Solitons are usually attributed to integrable systems. In this instance, solitons remain unchanged during interactions, apart from a phase shift. They can be viewed as ‘modes’ of the system, and, along with radiation modes, they can be used to solve initial-value problems using a nonlinear superposition of the modes [1]. However, in the recent years, the notion of solitons has been extended to various systems which are not necessarily integrable. Following this new trend, we extend the notion of solitons and include a wider range of systems in our treatment. These include dissipative systems, Hamiltonian systems and a particular case of them, viz. integrable systems.

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Authors and Affiliations

  1. Australian Photonics CRC, Optical Sciences Centre, Research School of Physical Sciences and Engineering, The Australian National University, ACT 0200, Canberra, Australia

    Nail Akhmediev

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  1. Nail Akhmediev
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Editors and Affiliations

  1. Joule Laboratory, Department of Physics, University of Salford, Salford, UK

    A. D. Boardman

  2. Radiophysics Department, Physics Faculty, Moscow State University, Moscow, Russia

    A. P. Sukhorukov

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Akhmediev, N. (2001). General Theory of Solitons. In: Boardman, A.D., Sukhorukov, A.P. (eds) Soliton-driven Photonics. NATO Science Series, vol 31. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0682-8_44

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  • DOI: https://doi.org/10.1007/978-94-010-0682-8_44

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