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Rok vydání:
2000
Identifikátory:
9780817636357
Table of Contents
Introduction
Part I: An Early History of the Soliton Chapter 1. A Century and a Half Ago Beginning of the Wave Theory The Brothers Weber Study Waves in Water From Waves in Water to Waves in Ether Scientific Discoveries - Mainstream and Ahead of Time Science and Society Chapter 2. The Great Solitary Wave of John Scott Russell Before the Fateful Encounter John Russell Meets the Solitary Wave That is Impossible! All the Same it Exists! Rehabilitation of the Solitary Wave The Solitary Wave in Solitude Wave or Particle? Chapter 3. Relatives of the Soliton Hermann Helmholtz and the Nerve Pulse Further Adventures with the Nerve Pulse Hermann Helmholtz and Eddies Lord Kelvin's "Vortex Atoms" Lord Ross and Vortices in Space About Linearity and Nonlinearity
Part II: Nonlinear Oscillations and Waves Chapter 4. A Portrait of the Pendulum The Equation of the Pendulum Small Oscillations of the Pendulum Galileo Galilei's Pendulum About Similarity and Dimensions Energy Conservation Language of Phase Diagrams Digression on Celestial Mechanics, Perturbations, and Stability Phase Portraits Phase Portrait of the Pendulum "Soliton" Solution of the Pendulum Equations Motions of the Pendulum and "Tame" Soliton Concluding Remarks Chapter 5. From Pendulum to Waves and Solitons Waves in Chains of Bound Particles Finding Modes in Chains of Particles-Important Mathematical Exercise A Historic Digression: Bernoulli Family and Waves D'Alembert's Waves and Debates on Them On Discrete and Continuous Speed of Sound and How it was Measured Dispersion in Chains of Atoms Of How to "Perceive" the Fourier Expansion Dispersion of Waves on Water Surfaces On the Speed of a Pack of Waves How Much Energy is Stored in a Wave?
Part III: Present and Future of Solitons Chapter 6. Frenkel's Solitons What is Theoretical Physics? Ya. I. Frenkel's Ideas Atomic Model of the Moving Dislocation after Frenkel and Kontorova Interactions between Dislocations "Live" Solitonic Atom Dislocations and Pendulum The Fate of the Waves of Sound Let us Have a Look at Dislocations Desktop Solitons Other Close Relatives of Dislocations: Mathematical Branch Magnetic Solitons Chapter 7. Rebirth of the Soliton Can Men be on Friendly Terms with the Computer? Many-faceted Chaos Enrico Fermi is Astonished by the Computer Russell's Soliton Returns Ocean Solitons: Tsunami, the Tenth Wave Three Solitons Soliton Telegraph The Nerve Impulse - "Elementary Particle of Thought" Vortices - Everywhere Chapter 8. Modern Solitons Modern Solitons Vortices in Superfluids Josephson Solitons Elementary Particles and Solitons Theories of Everything and Strings
Appendix I: Lord Kelvin "On Ship Waves" Appendix II: Skyrme's Soliton Appendix III: Mathematics Subject Index Name Index
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