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Physics of Solitons

ISBN-10: 0521854210

ISBN-13: 9780521854214

Edition: 2005

Authors: Thierry Dauxois, Michel Peyrard

List price: $124.00
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Description:

'Physics of Solitons' introduces the main basic properties of solitons using examples from macroscopic physics. It then presents the main theoretical methods before discussing applications from solid state or atomic physics.
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Book details

List price: $124.00
Copyright year: 2005
Publisher: Cambridge University Press
Publication date: 3/9/2006
Binding: Hardcover
Pages: 436
Size: 7.00" wide x 9.50" long x 0.75" tall
Weight: 2.244
Language: English

List of Portraits
Preface
Different classes of solitons
Introduction
Nontopological solitons: the Korteweg-de Vries equation
The discovery
The solutions of the KdV equation
Conservation rules
Nonlinear electrical lines
Blood pressure waves
Internal waves in oceanography
Generality of the KdV equation
Topological solitons: the sine-Gordon equation
A simple mechanical example: the chain of coupled pendula
Solutions of the sine-Gordon equation
Long Josephson junctions
Other examples of topological solitons
Envelope solitons and nonlinear localisation: the nonlinear Schrodinger equation
Nonlinear waves in the pendulum chain: the NLS equation
Properties of the nonlinear Schrodinger equation
Conservation laws
Noether's theorem
Nonlinear electrical lines
Solitons in optical fibres
Self-focusing in optics: the NLS equation in two space dimensions
Conclusion
The modelling process: ion acoustic waves in a plasma
Introduction
The plasma
Study of the linear dynamics
Nonlinear study
Derivation of the nonlinear Schrodinger equation
Experimental observations
Discussion
Mathematical methods for the study of solitons
Introduction
Linearisation around the soliton solution
Spectrum of the excitations around a sine-Gordon soliton
Application: perturbation of a soliton
Spectrum of the excitations around a [phi superscript 4] soliton
Collective coordinate method
Sine-Gordon soliton interacting with an impurity: effective Lagrangian method
Improving the method with a second collective coordinate
The inverse-scattering transform
Inverse scattering transform for the KdV equation
The inverse scattering transform: a 'nonlinear Fourier analysis'
Examples in solid state and atomic physics
Introduction
The Fermi-Pasta-Ulam problem
The physical question
Fermi, Pasta and Ulam: the characters
The solution of the FPU problem
Kruskal and Zabusky: the pioneers
FPU and the Japanese School
A simple model for dislocations in crystals
Plastic deformation of crystals
A one-dimensional model: the Frenkel-Kontorova model
Continuum limit approximation: the sine-Gordon equation
Are dislocations solitons?
Applications
Ferroelectric domain walls
Ferroelectric materials
A one-dimensional ferroelectric model
Structure of the domain walls in the continuum limit approximation
Dielectric response of a ferroelectric material
Thermodynamics of a nonlinear system
Incommensurate phases
Examples in solid state physics
A one-dimensional model for incommensurate phases: the Frenkel-Kontorova model
Commensurate phases
The commensurate-incommensurate transition
Structure of the incommensurate phase
Calculation of [delta subscript c]
Phase diagram
Dynamics of the incommensurate phase
Formation of the discommensurations
Conclusion
Solitons in magnetic systems
Ferromagnetism and antiferromagnetism
Equations for the dynamics of a spin chain
Magnons and solitons
Validity of the sine-Gordon approximation
Solitons in antiferromagnetic spin chains
Conclusion
Solitons in conducting polymers
Materials
The physical model of polyacetylene
The ground state of polyacetylene
The excited state of polyacetylene: the soliton solution
Mechanism of electric conduction in conducting polyacetylene
An experimental test for the presence of solitons
The other nonlinear excitations of polyacetylene
Solitons in Bose-Einstein condensates
Introduction
Theoretical description of a condensate
Magnetic traps
Dynamic properties
Soliton solutions
Nonlinear excitations in biological molecules
Introduction
Energy localisation and transfer in proteins
The mechanism proposed by Davydov
The Davydov equations
Does the Davydov soliton exist?
A model physical system: the acetanilide crystal
Nonlinear dynamics and statistical physics of DNA
A simple DNA model
Nonlinear dynamics of DNA
Statistical physics of DNA thermal denaturation
Stability of a domain wall: another approach to denaturation
Conclusion: Physical solitons: do they exist?
Appendices
Derivation of the KdV equation for surface hydrodynamic waves
Basic equations and boundary conditions
Mathematical formulation of the problem
The linear limit
The nonlinear equation in shallow water
Mechanics of a continuous medium
Lagrangian formalism
Hamiltonian formalism
Coherent states of a harmonic oscillator
References
Index