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The sine-Gordon Model and its Applications

From Pendula and Josephson Junctions to Gravity and High-Energy Physics

  • Book
  • © 2014

Overview

Editors:
  1. Jesús Cuevas-Maraver

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

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  2. Panayotis G. Kevrekidis

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

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    You can also search for this editor in PubMed   Google Scholar

  3. Floyd Williams

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

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  • Describes a wide range of applications including coupled torsion pendula and Josephson junction arrays and gravitational and high-energy physics
  • Presents the current state of the art in sine-Gordon research
  • Provides quick access to different aspects of the model and its applications
  • Includes a wide range of recent developments, including experimental ones, which no other book on this topic has incorporated in the past 20 years

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

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xiii
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  2. The sine-Gordon Model: General Background, Physical Motivations, Inverse Scattering, and Solitons

    • Boris A. Malomed
    Pages 1-30

  3. sine-Gordon Equation: From Discrete to Continuum

    • M. Chirilus-Bruckner, C. Chong, J. Cuevas-Maraver, P. G. Kevrekidis
    Pages 31-57

  4. Soliton Collisions

    • Sergey V. Dmitriev, Panayotis G. Kevrekidis
    Pages 59-85

  5. Effects of Radiation on sine-Gordon Coherent Structures in the Continuous and Discrete Cases

    • Luis A. Cisneros-Ake, A. A. Minzoni
    Pages 87-110

  6. Experimental Results for the sine-Gordon Equation in Arrays of Coupled Torsion Pendula

    • Lars Q. English
    Pages 111-129

  7. Soliton Ratchets in sine-Gordon-Like Equations

    • Niurka R. Quintero
    Pages 131-154

  8. The sine-Gordon Equation in Josephson-Junction Arrays

    • Juan J. Mazo, Alexey V. Ustinov
    Pages 155-175

  9. Some Selected Thoughts Old and New on Soliton-Black Hole Connections in 2d Dilaton Gravity

    • Floyd L. Williams
    Pages 177-205

  10. Dressing with Control: Using Integrability to Generate Desired Solutions to Einstein’s Equations

    • Shabnam Beheshti, Shadi Tahvildar-Zadeh
    Pages 207-231

  11. A Planar Skyrme-Like Model

    • Ramón J. Cova
    Pages 233-260

  12. Back Matter

    Pages 261-263
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Keywords

About this book

The sine-Gordon model is a ubiquitous model of Mathematical Physics with a wide range of applications extending from coupled torsion pendula and Josephson junction arrays to gravitational and high-energy physics models. The purpose of this book is to present a summary of recent developments in this field, incorporating both introductory background material, but also with a strong view towards modern applications, recent experiments, developments regarding the existence, stability, dynamics and asymptotics of nonlinear waves that arise in the model. This book is of particular interest to a wide range of researchers in this field, but serves as an introductory text for young researchers and students interested in the topic. The book consists of well-selected thematic chapters on diverse mathematical and physical aspects of the equation carefully chosen and assigned.

Reviews

“With the emphasis on the applications, the goal of the authors is to highlight a few important aspects of the sine-Gordon story in the form of concise mini-reviews. … any students and researchers interested in the integrable world may find enough motivations and backround material for further study of the dynamical systems admitting soliton solutions.” (Béla Gábor Pusztai, Acta Scientiarum Mathematicarum, Vol. 82 (1-2), 2016)

Editors and Affiliations

  • Departamento de Físíca Aplicada I, University of Sevilla, Sevilla, Spain

    Jesús Cuevas-Maraver

  • Mathematics and Statistics, University of Massachusetts, Amherst, USA

    Panayotis G. Kevrekidis, Floyd Williams

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