The Sine-Gordon Model and Its Applications: From Pendula and Josephson Junctions to Gravity and High-Energy Physics

ISBN-13: 9783319379890 / Angielski / Miękka / 2016 / 263 str.

Jesus Cuevas-Maraver; Panayotis Kevrekidis; Floyd Williams

Opis

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.

Recenzje

"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)

Spis treści

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.

Blurb

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.