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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
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.
Content Level »Research
Keywords »Arrays of Coupled Torsion Pendula - Black Hole Connections in 2d Dilaton Gravity - Desired Solutions to Einstein's Equations - Inverse Scattering - Josephson-junction Arrays - Planar Skyrme-like Model - Sine-Gordon Model - Soliton Ratchets - Solitons Collisions - Traveling Kink Problem
The sine-Gordon Model: General Background, Physical Motivations, Inverse Scattering, and Solitons.- Sine-Gordon Equation: From Discrete to Continuum.- Soliton Collisions.- The Traveling Kink Problem: Radiation Phenomena, Resonances, Pinning and How to Avoid It.- Experimental Results for the sine-Gordon Equation in Arrays of Coupled Torsion Pendula.- Soliton Ratchets in sine-Gordon-like Equations.- The sine-Gordon Equation in Josephson-Junction Arrays.- Some Selected Thoughts Old and New on Soliton - Black Hole Connections in 2d Dilaton Gravity.- Dressing with Control: Using Integrability to Generate Desired Solutions to Einstein's Equations.- A Planar Skyrme-like Model.