Physics of Solitons

This textbook gives an instructive view of solitons and their applications for advanced students of physics.

Thierry Dauxois (Author), Michel Peyrard (Author)

9780521143608, Cambridge University Press

Paperback, published 10 June 2010

436 pages
24.4 x 17 x 2.3 cm, 0.58 kg

Solitons are waves with exceptional stability properties which appear in many areas of physics. The basic properties of solitons are introduced here using examples from macroscopic physics (e.g. blood pressure pulses and fibre optical communications). The book then presents the main theoretical methods before discussing applications from solid state or atomic physics such as dislocations, excitations in spin chains, conducting polymers, ferroelectrics and Bose–Einstein condensates. Examples are also taken from biological physics and include energy transfer in proteins and DNA fluctuations. Throughout the book the authors emphasise a fresh approach to modelling nonlinearities in physics. Instead of a perturbative approach, nonlinearities are treated intrinsically and the analysis based on the soliton equations introduced in this book. Based on the authors' graduate course, this textbook gives an instructive view of the physics of solitons for students with a basic knowledge of general physics, and classical and quantum mechanics.

List of Portraits
Preface
Part I. Different Classes of Solitons: Introduction
1. Nontopological solitons: the Korteweg-de Vries equation
2. Topological soltitons: sine-Gordon equation
3. Envelope solitons and nonlinear localisation: the nonlinear Schrödinger equation
4. The modelling process: ion acoustic waves in a plasma
Part II. Mathematical Methods for the Study of Solitons: Introduction
5. Linearisation around the soliton solution
6. Collective coordinate method
7. The inverse-scattering transform
Part III. Examples in Solid State and Atomic Physics: Introduction
8. The Ferm–Pasta–Ulam problem
9. A simple model for dislocations in crystals
10. Ferroelectric domain walls
11. Incommensurate phases
12. Solitons in magnetic systems
13. Solitons in Conducting polymers
14. Solitons in Bose–Einstein condensates
Part IV. Nonlinear Excitations in Biological Molecules: Introduction
15. Energy localisation and transfer in proteins
16. Nonlinear dynamics and statistical physics of DNA
Conclusion: Physical solitons: do they exist?
Part V. Appendices: A. Derivation of the KdV equation for surface hydrodynamic waves
B. Mechanics of a continuous medium
C. Coherent states of an harmonic oscillator
References
Index.

Subject Areas: Mechanics of fluids [TGMF], Fluid mechanics [PHDF], Nonlinear science [PBWR]