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Introduction to the mathematical physics of nonlinear waves
Title statement Introduction to the mathematical physics of nonlinear waves / Minoru Fujimoto. [elektronický zdroj] Publication San Rafael [California] (40 Oak Drive, San Rafael, CA, 94903, USA) : Morgan & Claypool Publishers, [2014] Distribution Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2014] Phys.des. 1 online resource (various pagings) : illustrations. ISBN 9781627052764 (online) Note "Version: 20140301"--Title page verso. "A Morgan & Claypool publication as part of IOP Concise Physics"--Title page verso. Internal Bibliographies/Indexes Note Includes bibliographical references. Contents Introduction -- Preface Content note 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 -- Schr?odinger's equation -- Scattering by the potential V(x) = V b0 s sech p2 s 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 Schr?odinger equation. The 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 pseudopotential. Miscellaneous applications -- Surface waves -- Vortex motion in fluid media -- Plasma oscillation -- Laser light transmission through absorbing media -- Periodic lattices. Notes to Availability Full-text restricted to subscribers or individual document purchasers.. Přístup pouze pro oprávněné uživatele Note Způsob přístupu: World Wide Web.. Požadavky na systém: Adobe Acrobat Reader. Another responsib. Morgan & Claypool Publishers, Institute of Physics (Great Britain), Subj. Headings Nonlinear waves. * Nonlinear wave equations. * Mathematical physics. * Mathematical Physics. * SCIENCE / Physics / Mathematical & Computational. Form, Genre elektronické knihy electronic books Country Kalifornie Language angličtina Document kind Electronic books URL Plný text pro studenty a zaměstnance UPOL 
book
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.
Introduction -- PrefaceNonlinearity 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) = V b0 s sech p2 s 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.
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