1. Nonlinearity and elliptic functions in classical mechanics -- 1.1. A pendulum -- 1.2. Vibration by a nonlinear spring force -- 1.3. Hyperbolic and elliptic functions -- 1.4. A jumping rope -- 1.5. Variation principle -- 1.6. Buckling of an elastic rod 2. Wave propagation, singularities, and boundary conditions -- 2.1. Elastic waves along a linear string in infinite length -- 2.2. Microwave transmission -- 2.3. Wave equations -- 2.4. Sound propagation in air -- 2.5. Asymptotic approximation in air space 3. Order variables for structural phase transitions -- 3.1. Symmetry group in crystals -- 3.2. Solitons and the Ising model for pseudospin correlations -- 3.3. Macroscopic views of structural phase transitions -- 3.4. Observing critical anomalies 4. Soft modes of lattice displacements -- 4.1. The Lyddane-Sachs-Teller relation -- 4.2. Soft modes in perovskite oxides -- 4.3. Dynamics of soft modes -- 4.4. Soft-mode frequency in modulated crystals -- 4.5. Optical studies on symmetry changes at critical temperature 5. Nonlinearity development in crystals : Korteweg-deVries' equation for collective order variables and the complex potential -- 5.1. The Korteweg-deVries equation -- 5.2. Thermal solution for the Weiss potential -- 5.3. Condensate pinning by the Weiss potential -- 5.4. Nonlinear waves and complex lattice potentials -- 5.5. The complex lattice potential -- 5.6. Isothermal phase transition and entropy production 6. Soliton mobility in time-temperature conversion for thermal processes : Riccati's theorem -- 6.1. Bargmann's theorem -- 6.2. Riccati's theorem and the modified Korteweg-deVries equation -- 6.3. Soliton mobility studied by computational analysis 7. Toda's lattice of correlation potentials -- 7.1. The Toda soliton lattice -- 7.2. Developing nonlinearity -- 7.3. Conversion to Korteweg-deVries' lattice potential 8. Scattering theory of the soliton lattice -- 8.1. Elemental waves -- 8.2. Scattering theory : dissipation, reflection, and transmission -- 8.3. Method of inverse scattering -- 8.4. Entropy production from soliton potentials 9. Pseudopotentials and sine-Gordon equation : topological correlations in domain structure -- 9.1. Pseudopotentials in mesoscopic phases -- 9.2. The sine-Gordon equation -- 9.3. Phase solitons in adiabatic processes -- 9.4. The B�acklund transformation and domain boundaries -- 9.5. Computational studies of the B�acklund transformation 10. Trigonal structural transitions : domain stability in topological order -- 10.1. The sine-Gordon equation -- 10.2. Observing adiabatic fluctuations -- 10.3. Toda's theory of domain stability -- 10.4. Kac's theory of nonlinearity for domain disorder -- 10.5. Domain separation and thermal and quasi-adiabatic transitions -- 10.6. Mesoscopic domains in topological disorder 11. Soliton theory of superconducting transitions -- 11.1. The Meissner effect and Fr�ohlich's proposal -- 11.2. Magnetic images of Fr�ohlich's interaction -- 11.3. The Cooper pair and persistent current -- 11.4. Critical temperatures and energy gap in superconducting transitions -- 11.5. Anderson's theory of superconducting phase transitions -- 11.6. Cuprate-layer structure and the Cooper pair -- 11.7. Meissner's effect in cuprate-layers and metallic hydrogen sulfide H3S 12. Irreducible thermodynamics of superconducting phase transitions -- 12.1. Superconducting phase transition -- 12.2. Electromagnetic properties of superconductors -- 12.3. The Ginzburg-Landau equation for superconducting phase transitions -- 12.4. Field theory of superconducting transitions.
Written for students at upper-undergraduate and graduate levels, it is suitable for advanced physics courses on nonlinear physics. The book covers the fundamental properties of nonlinear waves, dealing with both theory and experiment. The aim is to emphasize established tools and introduce new methods underpinning important new developments in this field, especially as applied to solid-state materials. The updated edition has been extended to emphasize the importance of thermodynamics in a description of modulated crystals and contains new chapters on superconductivity that can be interpreted by the soliton mechanism. It is also updated to include new end-of-chapter problems.
Graduate students in physics and mathematical physics.
Mode of access: World Wide Web. System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.
Minoru Fujimoto is a retired professor from the University of Guelph, Canada, where he conducted research in the field of magnetic resonance studies on structural phase transitions in crystals which has currently been extended to theoretical work with soliton dynamics especially as applied to crystalline condensed matter systems. He is the author of numerous papers and several books including Physics of Classical Electromagnetism and Thermodynamics of Crystalline States (Springer); Introduction to Mathematical Physics of Nonlinear Waves and Solitons in Crystalline Processes (IOP Publishing). He lives in Mississauga, Ontario.
9780750337595 9780750337588
10.1088/978-0-7503-3759-5 doi
Nonlinear waves. Nonlinear theories. Mathematical physics. Mathematics and computation.