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© 2004

The Frenkel-Kontorova Model

Concepts, Methods, and Applications

Benefits

  • There is no competitive text to this book

  • Presents nonlinear dynamics and the interdisciplinary concepts of nonlinear science from a unifying point of view

  • Addresses researchers as well as non-specialists and graduate students

Book

Part of the Texts and Monographs in Physics book series (TMP)

Table of contents

  1. Front Matter
    Pages I-XVIII
  2. Oleg M. Braun, Yuri S. Kivshar
    Pages 1-8
  3. Oleg M. Braun, Yuri S. Kivshar
    Pages 9-30
  4. Oleg M. Braun, Yuri S. Kivshar
    Pages 31-98
  5. Oleg M. Braun, Yuri S. Kivshar
    Pages 99-140
  6. Oleg M. Braun, Yuri S. Kivshar
    Pages 141-194
  7. Oleg M. Braun, Yuri S. Kivshar
    Pages 195-242
  8. Oleg M. Braun, Yuri S. Kivshar
    Pages 243-290
  9. Oleg M. Braun, Yuri S. Kivshar
    Pages 291-342
  10. Oleg M. Braun, Yuri S. Kivshar
    Pages 343-364
  11. Oleg M. Braun, Yuri S. Kivshar
    Pages 365-382
  12. Oleg M. Braun, Yuri S. Kivshar
    Pages 383-430
  13. Oleg M. Braun, Yuri S. Kivshar
    Pages 431-434
  14. Alfred Seeger
    Pages 435-440
  15. Back Matter
    Pages 441-475

About this book

Introduction

This book presents an overview of the basic concepts, methods and applications of nonlinear low-dimensional solid-state physics based on the Frenkel--Kontorova model and its generalizations. It allows a nonspecialist to acquire foundations in the interdisciplinary concepts and methods of both solid-state physics and nonlinear science. It covers many important topics such as the nonlinear dynamics of discrete systems, the dynamics of solitons and their interaction, commensurate and incommensurate systems, statistical mechanics of nonlinear systems, ratchets, and nonequilibrium dynamics of interacting many-body systems. Also treated are the principal nonlinear equations along with the properties of their localized solutions and methods for their analysis.

 

Keywords

Breather DNA Dynamics Dislocation Dynamics Driven Dynamics Frenkel-Kontorova Model Kink Nonlinear Condensed Matter Physics REM Ratchet STEM Sine-Gordon Equation Thermalized Dynamics nonlinear dynamics

Authors and affiliations

  1. 1.Institute of PhysicsUkrainian Academy of SciencesKievUkraine
  2. 2.Research School of Physical Sciences and EngineeringAustralian National UniversityCanberraAustralia

Bibliographic information

Industry Sectors
Energy, Utilities & Environment

Reviews

From the reviews:

"[...] the book of Oleg Braun and Yury Kivshar deserves one's close attention and provides thorough insight into a well-known physical paradigm. The sheer fact of providing all this information in one piece of work deserves its own merit, and the contribution of the authors' own work bears its own value. The volume will undoubtedly prove to be a valuable source of information to researchers who are familiar with soliton theories, and will provide inspiration to those less familiar." (Physicalia 2005, 57, page 209)

"Braun and Kivshar have managed to write a comparatively compact and yet informative description of the FK model. It is stocked with a huge reference list that is invaluable for any serious researcher. The authors avoid delving into specific applications in order to concentrate on making transparent the fundamental physical concepts. Hence, the contents of the book should attract interest from both solid state physicists and researchers in the nonlinear sciences." (Contemporary Physics 2004, 45, page 537-538) 

"The book of Oleg Braun and Yury Kivshar deserves one’s close attention and provides thorough insight into a well-known physical paradigm. The sheer fact of providing all this information (previously dispersed among numerous technical articles) in one piece of work deserves its own merit, and the contribution of the author’s own work bears its own value. The volume will undoubtedly prove to be a valuable source of information to researchers who are familiar with soliton theories, and will provide inspiration to those less familiar." (Ioannis Kourakis, Physicalia, Vol. 57 (3), 2005)

"The book has thirteen chapters. … It is stocked with a huge reference list that is invaluable for any serious researcher. The authors avoid delving into specific applications in order to concentrate on making transparent the fundamental physical concepts. Hence, the contents of the book should attract interest from both solid state physicists and researchers in the nonlinear sciences." (J. Hartley, Contemporary Physics, Vol. 45 (6), 2004)