Introduction to the mathematical physics of nonlinear waves /

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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 metho...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Fujimoto, Minoru (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2021]
Edición:Second edition.
Colección:IOP (Series). Release 21.
IOP ebooks. 2021 collection.
Temas:
Nonlinear waves.
Nonlinear theories.
Mathematical physics.
Mathematics and computation.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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 Bäcklund transformation and domain boundaries
  • 9.5. Computational studies of the Bäcklund 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 Fröhlich's proposal
  • 11.2. Magnetic images of Fröhlich'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.

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