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
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. The book 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, and nonequilibrium dynamics of interacting many-body systems.
1 Introduction.- 2 Physical Models.- 3 Kinks.- 4 Breathers.- 5 Ground State.- 6 Statistical Mechanics.- 7 Thermalized Dynamics.- 8 Driven Dynamics.- 9 Ratchets.- 10 Finite-Length Chain.- 11 Two-Dimensional Models.- 12 Conclusion.- 13 Historical Remarks.- References.
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.
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 deillegalscription 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)
Theoretical physics deals with physical models. The main requirements for a good physical model are simplicity and universality. Universal models which can be applied to describe a variety of different phenomena are very rare in physics and, therefore, they are of key importance. Such models attract the special attention of researchers as they can be used to describe underlying physical concepts in a simple way. Such models appear again and again over the years and in various forms, thus extending their applicability and educa tional value. The simplest example of this kind is the model of a pendulum; this universal model serves as a paradigm which encompasses basic features of various physical systems, and appears in many problems of very different physical context. Solids are usually described by complex models with many degrees of freedom and, therefore, the corresponding microscopic equations are rather complicated. However, over the years a relatively simple model, known these days as the Prenkel-K ontorova model, has become one of the fundamental and universal tools of low-dimensional nonlinear physics; this model describes a chain of classical particles coupled to their neighbors and subjected to a pe riodic on-site potential.
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 deillegalscription 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 attractinterest from both solid state physicists and researchers in the nonlinear sciences." (J. Hartley, Contemporary Physics, Vol. 45 (6), 2004)
Inhaltsverzeichnis
1 Introduction.- 2 Physical Models.- 3 Kinks.- 4 Breathers.- 5 Ground State.- 6 Statistical Mechanics.- 7 Thermalized Dynamics.- 8 Driven Dynamics.- 9 Ratchets.- 10 Finite-Length Chain.- 11 Two-Dimensional Models.- 12 Conclusion.- 13 Historical Remarks.- References.
Klappentext
Theoretical physics deals with physical models. The main requirements for a good physical model are simplicity and universality. Universal models which can be applied to describe a variety of different phenomena are very rare in physics and, therefore, they are of key importance. Such models attract the special attention of researchers as they can be used to describe underlying physical concepts in a simple way. Such models appear again and again over the years and in various forms, thus extending their applicability and educa tional value. The simplest example of this kind is the model of a pendulum; this universal model serves as a paradigm which encompasses basic features of various physical systems, and appears in many problems of very different physical context. Solids are usually described by complex models with many degrees of freedom and, therefore, the corresponding microscopic equations are rather complicated. However, over the years a relatively simple model, known these days as the Prenkel-K ontorova model, has become one of the fundamental and universal tools of low-dimensional nonlinear physics; this model describes a chain of classical particles coupled to their neighbors and subjected to a pe riodic on-site potential.
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. The book 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, and nonequilibrium dynamics of interacting many-body systems.
