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.
Author(s): Jesús Cuevas-Maraver, Panayotis G. Kevrekidis, Floyd Williams (eds.)
Series: Nonlinear Systems and Complexity 10
Edition: 1
Publisher: Springer International Publishing
Year: 2014
Language: English
Pages: 263
Tags: Theoretical, Mathematical and Computational Physics; Mathematical Physics; Mechanics; Astrophysics and Astroparticles; Particle and Nuclear Physics
Front Matter....Pages i-xiii
The sine-Gordon Model: General Background, Physical Motivations, Inverse Scattering, and Solitons....Pages 1-30
sine-Gordon Equation: From Discrete to Continuum....Pages 31-57
Soliton Collisions....Pages 59-85
Effects of Radiation on sine-Gordon Coherent Structures in the Continuous and Discrete Cases....Pages 87-110
Experimental Results for the sine-Gordon Equation in Arrays of Coupled Torsion Pendula....Pages 111-129
Soliton Ratchets in sine-Gordon-Like Equations....Pages 131-154
The sine-Gordon Equation in Josephson-Junction Arrays....Pages 155-175
Some Selected Thoughts Old and New on Soliton-Black Hole Connections in 2d Dilaton Gravity....Pages 177-205
Dressing with Control: Using Integrability to Generate Desired Solutions to Einstein’s Equations....Pages 207-231
A Planar Skyrme-Like Model....Pages 233-260
Back Matter....Pages 261-263
