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The sine-Gordon Model: General Background, Physical Motivations, Inverse Scattering, and Solitons

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The sine-Gordon Model and its Applications

Part of the book series: Nonlinear Systems and Complexity ((NSCH,volume 10))

Abstract

This chapter offers an overview of the vast research area developed around the sine-Gordon (sG) equation, including solution methods and various nonlinear modes generated by this equation, viz., topological and dynamical solitons (kinks and breathers), cnoidal waves (chains of kinks), and others. Also included is a survey of physical applications of the sG equation, and an outline of the perturbation theory used for the analysis of physical models based on the sG equation but differing from the ideal integrable form of this equation. Topics presented in the chapter, with some details or in a brief form, are the inverse scattering, transform and the perturbation theory based on it, the Bäcklund transform, energy- and momentum-balance methods for the analysis of the soliton dynamics in perturbed versions of the sG equation, the double sG equation, quantum sG systems, multidimensional sG equations, systems of coupled sG equations, and others.

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Authors and Affiliations

  1. Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv, 69978, Israel

    Boris A. Malomed

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  1. Boris A. Malomed
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Correspondence to Boris A. Malomed .

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Editors and Affiliations

  1. Departamento de Físíca Aplicada I, University of Sevilla, Sevilla, Spain

    Jesús Cuevas-Maraver

  2. Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts, USA

    Panayotis G. Kevrekidis

  3. Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts, USA

    Floyd Williams

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Malomed, B.A. (2014). The sine-Gordon Model: General Background, Physical Motivations, Inverse Scattering, and Solitons. In: Cuevas-Maraver, J., Kevrekidis, P., Williams, F. (eds) The sine-Gordon Model and its Applications. Nonlinear Systems and Complexity, vol 10. Springer, Cham. https://doi.org/10.1007/978-3-319-06722-3_1

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  • DOI: https://doi.org/10.1007/978-3-319-06722-3_1

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