Introduction to the mathematical physics of nonlinear waves /

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Nonlinear physics is a well-established discipline in physics today, and this book offers a comprehensive account of the basic soliton theory and its applications. Although primarily mathematical, the theory for nonlinear phenomena in practical environments needs to be understood at upper undergradu...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Fujimoto, Minoru (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: San Rafael [California] (40 Oak Drive, San Rafael, CA, 94903, USA) : Morgan & Claypool Publishers, [2014]
Colección:IOP concise physics,
IOP (Series). Release 1.
Temas:
Nonlinear waves.
Nonlinear wave equations.
Mathematical physics.
Mathematical Physics.
SCIENCE / Physics / Mathematical & Computational.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Nonlinearity in classical mechanics
  • A pendulum
  • Vibration by a nonlinear spring force
  • A jumping rope
  • Hyperbolic and elliptic functions
  • Variation principle
  • Buckling deformation of a rod
  • Wave propagation, singularities and boundaries
  • Elastic waves along a linear string of infinite length
  • Microwave transmission
  • Schrödinger's equation
  • Scattering by the potential V(x) = V₀ sech² x
  • Two-dimensional waves in inhomogeneous medium
  • Sound propagation in air
  • Solitons and adiabatic potentials
  • The Korteweg-deVries equation
  • Steady solutions of the Korteweg-deVries equation
  • Developing equations of nonlinear vector waves
  • Bargmann's theorem
  • Riccati's theorem
  • Properties of the Eckart potential in the soliton field
  • Zabusky-Kruskal's computational analysis
  • Structural phase transitions
  • Initial uncertainties and transition anomalies
  • Dynamical theory of collective motion
  • Pseudopotential and sine-Gordon equation
  • Nonlinear waves
  • Elemental waves
  • Matrix formulation for nonlinear development
  • Heat dissipation of wave motion
  • Born-Huang transitions in crystals
  • Symmetry of media for the Korteweg-deVries equation
  • Soliton description
  • Scattering theory
  • One-component waves
  • Two-component scatterings
  • Method of inverse scatterings
  • Coherent wave packets and Marchenko's equation
  • Reflectionless multi-soliton potentials
  • Two-component systems
  • Quasi-static soliton states
  • Developing the Korteweg-deVries equation
  • Multi-soliton potentials in unsteady states
  • The modified Korteweg-deVries equation, part 2
  • Thermodynamic instability and Breezer potentials
  • The third-order Schrödinger equation
  • The Bäcklund transformation and sine-Gordon equations
  • The Klein-Gordon equation
  • The Bäcklund transformation
  • The sine-Gordon equation
  • Numerical analysis of the sine-Gordon equation
  • Inverse scatterings and the Bäcklund transformation
  • Scatterings by a pseudopotential
  • Miscellaneous applications
  • Surface waves
  • Vortex motion in fluid media
  • Plasma oscillation
  • Laser light transmission through absorbing media
  • Periodic lattices.

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