Introduction to the mathematical physics of nonlinear waves /

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"Version: 20140301"--Title page verso."A Morgan & Claypool publication as part of IOP Concise Physics"--Title page verso.Includes bibliographical references.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 rodWave propagation, singularities and boundaries -- Elastic waves along a linear string of infinite length -- Microwave transmission -- Schr?odinger's equation -- Scattering by the potential V(x) = Vb0s sechp2s x -- Two-dimensional waves in inhomogeneous medium -- Sound propagation in airSolitons 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 analysisStructural phase transitions -- Initial uncertainties and transition anomalies -- Dynamical theory of collective motion -- Pseudopotential and sine-Gordon equationNonlinear 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 descriptionScattering theory -- One-component waves -- Two-component scatteringsMethod of inverse scatterings -- Coherent wave packets and Marchenko's equation -- Reflectionless multi-soliton potentials -- Two-component systemsQuasi-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 Schr?odinger equationThe B?acklund transformation and sine-Gordon equations -- The Klein-Gordon equation -- The B?acklund transformation -- The sine-Gordon equation -- Numerical analysis of the sine-Gordon equation -- Inverse scatterings and the B?acklund transformation -- Scatterings by a pseudopotentialMiscellaneous applications -- Surface waves -- Vortex motion in fluid media -- Plasma oscillation -- Laser light transmission through absorbing media -- Periodic lattices.Full-text restricted to subscribers or individual document purchasers.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.Also available in print.Mode of access: World Wide Web.System requirements: Adobe Acrobat Reader.Minoru Fujimoto is a retired professor of the University of Guelph, Ontario, Canada. Engaged in experimental work on magnetic resonance on structural phase transitions, his books Physics of Classical Electromagnetism and Thermodynamics of Crystalline States were published by Springer.Title from PDF title page (viewed on March 28, 2014).

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: .,

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1 online resource (various pagings) :illustrations.

Language

English

ISBN/ISSN

9781627052764

Classification

530.155355

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Subject(s)

SCIENCE / Physics / Mathematical & Computational.
Mathematical physics.
Nonlinear waves.
Nonlinear wave equations.

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Statement of Responsibility

Minoru Fujimoto.

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