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.
Thierry Dauxois is a CNRS researcher at Ecole Normale Superieure de Lyon and an experienced author in his field. Professor Michel Peyrard works at Ecole Normale Superieure de Lyon, and a senior member of the Institut Universitaire de France.
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 Schroedinger 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.