Introduction to the mathematical physics of nonlinear waves için kapak resmi
Başlık:
Introduction to the mathematical physics of nonlinear waves
Dil:
English
ISBN:
9781627052764
Yayın Bilgileri:
San Rafael [California] (40 Oak Drive, San Rafael, CA, 94903, USA) : Morgan & Claypool Publishers, [2014]

Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2014]
Fiziksel Tanımlama:
1 online resource (various pagings) : illustrations.
Seri:
IOP concise physics,
Genel Not:
"Version: 20140301"--Title page verso.

"A Morgan & Claypool publication as part of IOP Concise Physics"--Title page verso.
İçerik:
Introduction -- Preface

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.
Özet:
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 undergraduate level, with particular attention given to the presence of media where nonlinearity takes place. This book addresses mathematical theories, but also suggests possible theoretical innovations for many issues, providing a stimulating reference for both students and researchers.

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E-Kitap 1830364-1001 QA927 .F845 2014 eb IOP E-Kitap Lokasyonu
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Özet

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 environment