The Versatile Soliton

Rok: 2000
ISBN: 9780817636357
OKCZID: 110238223

Citace (dle ČSN ISO 690):
FILIPPOV, Alexandre T. The versatile soliton. Boston: Birkhäuser, 2000. xiv, 261 s.

Hodnocení: 4.5 / 5 (6 hlasů)

Anotace

If you have not already heard about solitons, you will sooner or later encounter them. The soliton, a solitary wave impulse preserving its shape and strikingly similar to a particle, is one of the most fascinating and beautiful phenomena in the physics of nonlinear waves. In this engaging book, the concept of the soliton is traced from the beginning of the last century to modern times, with recent applications in biology, oceanography, solid state physics, electronics, elementary particle physics, and cosmology. The main concepts and results of theoretical physics related to solitons can be explained without using much mathematics. Indeed, on the descriptive and historical level, only some knowledge of high school physics and mathematics is needed. At a higher level, for understanding the elementary theory of oscillations and waves, the reader can intuit much from the numerous illustrations and perhaps skip the formulas presented. But to appreciate the deep connections in this book between apparently different and diverse phenomena and ideas, the reader must be able to follow elementary mathematical computations. Still more advanced mathematics is required for the appendices. 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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