Physics of Solitons
Cambridge University Press, 6/10/2010
EAN 9780521143608, ISBN10: 0521143608
Paperback, 436 pages, 24.4 x 17 x 2.3 cm
Language: English
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.