Solitons are exceptionally stable standing waves which appear in many areas of physics. This textbook introduces the basic properties of solitons using examples from macroscopic physics before presenting the main theoretical methods. It gives an instructive view of the physics of solitons, and their applications, for advanced students of physics.
Solitons are exceptionally stable standing waves which appear in many areas of physics. This textbook introduces the basic properties of solitons using examples from macroscopic physics before presenting the main theoretical methods. It gives an instructive view of the physics of solitons, and their applications, for advanced students of physics.
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.
Inhaltsangabe
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.
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.
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