Waves Called Solitons
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1 Waves Called Solitons Concepts and Experiments Bearbeitet von Michel Remoissenet überarbeitet Buch. XXIII, 328 S. Hardcover ISBN Format (B x L): 15,5 x 23,5 cm Gewicht: 1510 g Weitere Fachgebiete > Technik > Werkstoffkunde, Mechanische Technologie > Statik, Dynamik, Kinetik, Kinematik schnell und portofrei erhältlich bei Die Online-Fachbuchhandlung beck-shop.de ist spezialisiert auf Fachbücher, insbesondere Recht, Steuern und Wirtschaft. Im Sortiment finden Sie alle Medien (Bücher, Zeitschriften, CDs, ebooks, etc.) aller Verlage. Ergänzt wird das Programm durch Services wie Neuerscheinungsdienst oder Zusammenstellungen von Büchern zu Sonderpreisen. Der Shop führt mehr als 8 Millionen Produkte.
2 Contents 1 Basic Concepts and the Discovery of Solitons A look at linear and nonlinear signatures Discovery of the solitary wave Discovery of the soliton The soliton concept in physics Linear Waves in Electrical Transmission Lines Linear nondispersive waves Sinusoidal-wave characteristics Wave energy density and power The group-velocity concept Linear dispersive waves Dispersive transmission lines Electrical network The weakly dispersive limit Evolution of a wavepacket envelope Dispersion-induced wavepacket broadening Appendix 2A. General solution for the envelope evolution Appendix 2B. Evolution of the envelope of a Gaussian wavepacket Solitons in Nonlinear Transmission Lines Nonlinear and dispersionless transmission lines Combined effects of dispersion and nonlinearity Electrical solitary waves and pulse solitons Laboratory experiments on pulse solitons Experimental arrangement Series of experiments Experiments with a pocket version of the electrical network XIII
3 3.6 Nonlinear transmission lines in the microwave range Appendix 3A. Calculation of the effect of nonlinearity on wave propagation Appendix 3B. Derivation of the solitary-wave solution Appendix 3C. Derivation of the KdV equation and its soliton solution 62 Appendix 3D. Details of the electronics: switch driver and pulse generator More on Transmission-Line Solitons Lattice solitons in the electrical Toda network Lattice solitons Experiments on lattice solitons Collisions of two lattice solitons moving in opposite directions The Fermi-Pasta-Ulam recurrence phenomenon Periodic wavetrains in transmission lines The solitary wave limit and sinusoidal limit of the cnoidal wave Modulated waves and the nonlinear dispersion relation Envelope and hole solitons Experiments on envelope and hole solitons Modulational instability Laboratory experiments on modulational instability Model equations Experiments Modulational instability of two coupled waves Microwave solitons in magnetic transmission lines Nonlinear spin waves NLS model equation for spin waves Observation of magnetic envelope solitons Solitons and signal processing Appendix 4A. Periodic wavetrain solutions Appendix 4B. The Jacobi elliptic functions B.1 Asymptotic limits B.2 Derivatives and integrals Appendix 4C. Envelope and hole soliton solutions XIV
4 5 Hydrodynamic Solitons Equations for surface water waves Reduced fluid equations Small-amplitude surface gravity waves Linear shallow- and deep-water waves Shallow-water waves Deep-water waves Surface-tension effects: capillary waves Solitons in shallow water Experiments on solitons in shallow water Experimental arrangement Experiments Stokes waves and soliton wavepackets in deep water Stokes waves Soliton wavepackets Experiments on solitons in deep water Experiments on modulational instability in deep water Some applications of the KdV model Blood pressure wave propagation Nonlinear modes of liquid drops Appendix 5A. Basic equations of fluid mechanics A.1 Conservation of mass A.2 Conservation of momentum A.3 Conservation of entropy Appendix 5B. Basic definitions and approximations B.1 Streamline B.2 Irrotational and incompressible flow B.3 Two-dimensional flow: the stream function B.4 Boundary conditions B.5 Surface tension Appendix 5C. Derivation of the KdV equation: the perturbative approach Appendix 5D. Derivation of the nonlinear dispersion relation Appendix 5E. Details of the probes and the electronics XV
5 6 Mechanical Solitons An experimental mechanical transmisssion line General description of the line Construction of the line Mechanical kink solitons Linear waves in the low-amplitude limit Large amplitude waves: kink solitons Lorentz contraction of the kink solitons Particle properties of the kink solitons KinkÐkink and kinkðantikink collisions Breather solitons Experiments on kinks and breathers Helical waves, or kink array Dissipative effects Envelope solitons Lattice effects Pocket version of the pendulum chain, lattice effects Pendulum chain with weak coupling A mechanical tranmsission line with two equilibrium states Periodic and double-well substrate potentials General description of the mechanical chain Kink-soliton solutions Compacton-like kinks or compactons Experiments Solitons, compactons and nanopterons Appendix 6A. Kink-soliton and antikink-soliton solutions Appendix 6B. Calculation of the energy and the mass of a kink soliton Appendix 6C. Solutions for kink kink and kink antikink collisions, and breathers C.1 Kink solutions C.2 KinkÐkink collisions C.3 Breather solitons C.4 KinkÐantikink collision Appendix 6D. Solutions for helical waves Appendix 6E. Pendulum with torsion and gravity XVI
6 Appendix 6F Model equation for the pendulum chain Fluxons in Josephson Transmission Lines The Josephson effect in a short junction The small Josephson junction The long Josephson junction as a transmission line Dissipative effects Experimental observations of fluxons Indirect observation Direct observation Lattice effects Appendix 7A. Josephson equations Solitons in Optical Fibers Optical-fiber characteristics Linear dispersive effects Nonlinear effects Effect of losses Wave-envelope propagation Bright and dark solitons Bright solitons Dark solitons Experiments on optical solitons Perturbations and soliton communications Effect of losses Soliton communications Modulational instability of coupled waves A look at quantum-optical solitons Some other kinds of optical solitons: spatial solitons Appendix 8A. Electromagnetic equations in a nonlinear medium The Soliton Concept in Lattice Dynamics The one-dimensional lattice in the continuum approximation The quasi-continuum approximation for the monatomic lattice The Toda lattice Envelope solitons and localized modes XVII
7 9.5 The one-dimensional lattice with transverse nonlinear modes Motion of dislocations in a one-dimensional crystal The one-dimensional lattice model for structural phase transitions The orderðdisorder transition The displacive transition Kink-soliton solutions for generalized on-site potentials A lattice model with an exact kink-soliton solution Energy localization in nonlinear lattices Self-trapped states: polaron and conformon Intrinsic localized modes or discrete breathers Observation of discrete breathers Discrete pendulum chains Mechanical chain with torsion and gravity A chain of magnetic pendulums Appendix 9A. Solutions for transverse displacements Appendix 9B. Kink-soliton or domain-wall solutions Appendix 9C Construction of a double-well potential A Look at Some Remarkable Mathematical Techniques Lax equations and the inverse scattering transform method The Fourier-transform method for linear equations The Lax pair for nonlinear evolution equations The KdV equation and the spectral problem Time evolution of the scattering data Discrete eigenvalues Continuous spectrum The inverse scattering problem Discrete spectrum only: soliton solution Response of the KdV model to an initial disturbance The delta function potential The rectangular potential well The sech-squared potential well The inverse scattering transform for the NLS equation The Hirota method for the KdV equation The Hirota method for the NLS equation XVIII
8 11 Diffusive solitons Combined effects of dissipation and nonlinearity A diffusive electrical transmission line Linear diffusive waves Kink-shaped diffusive solitons Experiments on electrical diffusive solitons Reaction diffusion processes Reaction diffusion equations A chemical model with reaction diffusion An electrical lattice with reaction diffusion Experiments with an electrical lattice A mechanical analog with diffusive solitons Chain with flexion and gravity Experimental chain Reaction diffusion processes in lattices Propagation failure Discrete reaction diffusion model with exact solution Appendix 11A. Derivation of the Burgers equation Appendix 11B. Solution of the reaction diffusion equation Appendix 11C. Equation of motion of an Euler strut References Subject Index XIX
9 XX
Basic Concepts and the Discovery of Solitons p. 1 A look at linear and nonlinear signatures p. 1 Discovery of the solitary wave p. 3 Discovery of the
Basic Concepts and the Discovery of Solitons p. 1 A look at linear and nonlinear signatures p. 1 Discovery of the solitary wave p. 3 Discovery of the soliton p. 7 The soliton concept in physics p. 11 Linear
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