Global Propagation Of Regular Nonlinear Hyperbolic Waves
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Global Propagation Of Regular Nonlinear Hyperbolic Waves
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Author : Tatsien Li
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-09-01
Global Propagation Of Regular Nonlinear Hyperbolic Waves written by Tatsien Li and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-01 with Science categories.
This monograph describes global propagation of regular nonlinear hyperbolic waves described by first-order quasilinear hyperbolic systems in one dimension. The exposition is clear, concise, and unfolds systematically beginning with introductory material and leading to the original research of the authors. Topics are motivated with a number of physical examples from the areas of elastic materials, one-dimensional gas dynamics, and waves. Aimed at researchers and graduate students in partial differential equations and related topics, this book will stimulate further research and help readers further understand important aspects and recent progress of regular nonlinear hyperbolic waves.
Global Propagation Of Regular Nonlinear Hyperbolic Waves
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Author : Tatsien Li
language : en
Publisher: Birkhäuser
Release Date : 2011-11-02
Global Propagation Of Regular Nonlinear Hyperbolic Waves written by Tatsien Li and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-02 with Science categories.
This monograph describes global propagation of regular nonlinear hyperbolic waves described by first-order quasilinear hyperbolic systems in one dimension. The exposition is clear, concise, and unfolds systematically beginning with introductory material and leading to the original research of the authors. Topics are motivated with a number of physical examples from the areas of elastic materials, one-dimensional gas dynamics, and waves. Aimed at researchers and graduate students in partial differential equations and related topics, this book will stimulate further research and help readers further understand important aspects and recent progress of regular nonlinear hyperbolic waves.
Nonlinear Waves A Geometrical Approach
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Author : Angela Slavova
language : en
Publisher: World Scientific Publishing
Release Date : 2018-11-16
Nonlinear Waves A Geometrical Approach written by Angela Slavova and has been published by World Scientific Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-16 with Mathematics categories.
This volume provides an in-depth treatment of several equations and systems of mathematical physics, describing the propagation and interaction of nonlinear waves as different modifications of these: the KdV equation, Fornberg-Whitham equation, Vakhnenko equation, Camassa-Holm equation, several versions of the NLS equation, Kaup-Kupershmidt equation, Boussinesq paradigm, and Manakov system, amongst others, as well as symmetrizable quasilinear hyperbolic systems arising in fluid dynamics.Readers not familiar with the complicated methods used in the theory of the equations of mathematical physics (functional analysis, harmonic analysis, spectral theory, topological methods, a priori estimates, conservation laws) can easily be acquainted here with different solutions of some nonlinear PDEs written in a sharp form (waves), with their geometrical visualization and their interpretation. In many cases, explicit solutions (waves) having specific physical interpretation (solitons, kinks, peakons, ovals, loops, rogue waves) are found and their interactions are studied and geometrically visualized. To do this, classical methods coming from the theory of ordinary differential equations, the dressing method, Hirota's direct method and the method of the simplest equation are introduced and applied. At the end, the paradifferential approach is used.This volume is self-contained and equipped with simple proofs. It contains many exercises and examples arising from the applications in mechanics, physics, optics and, quantum mechanics.
Nonlinear Waves In Elastic Media
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Author : A.G. Kulikovskii
language : en
Publisher: CRC Press
Release Date : 2021-07-01
Nonlinear Waves In Elastic Media written by A.G. Kulikovskii and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-01 with Mathematics categories.
Nonlinear Waves in Elastic Media explores the theoretical results of one-dimensional nonlinear waves, including shock waves, in elastic media. It is the first book to provide an in-depth and comprehensive presentation of the nonlinear wave theory while taking anisotropy effects into account. The theory is completely worked out and draws on 15 years of research by the authors, one of whom also wrote the 1965 classic Magnetohydrodynamics. Nonlinear Waves in Elastic Media emphasizes the behavior of quasitransverse waves and analyzes arbitrary discontinuity disintegration problems, illustrating that the solution can be non-unique - a surprising result. The solution is shown to be especially interesting when anisotropy and nonlinearity effects interact, even in small-amplitude waves. In addition, the text contains an independent mathematical chapter describing general methods to study hyperbolic systems expressing the conservation laws. The theoretical results described in Nonlinear Waves in Elastic Media allow, for the first time, discovery and interpretation of many new peculiarities inherent to the general problem of discontinuous solutions and so provide a valuable resource for advanced students and researchers involved with continuum mechanics and partial differential equations.
Wave Propagation In Linear And Nonlinear Periodic Media
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Author : Francesco Romeo
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-07-30
Wave Propagation In Linear And Nonlinear Periodic Media written by Francesco Romeo and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-30 with Technology & Engineering categories.
Waves and defect modes in structures media.- Piezoelectric superlattices and shunted periodic arrays as tunable periodic structures and metamaterials.- Topology optimization.- Map-based approaches for periodic structures.- Methodologies for nonlinear periodic media. The contributions in this volume present both the theoretical background and an overview of the state-of-the art in wave propagation in linear and nonlinear periodic media in a consistent format. They combine the material issued from a variety of engineering applications, spanning a wide range of length scale, characterized by structures and materials, both man-made and naturally occurring, featuring geometry, micro-structural and/or materials properties that vary periodically in space, including periodically stiffened plates, shells and beam-like as well as bladed disc assemblies, phononic metamaterials, photonic crystals and ordered granular media. Along with linear models and applications, analytical methodologies for analyzing and exploiting complex dynamical phenomena arising in nonlinear periodic systems are also presented.
Propagation Of Multidimensional Nonlinear Waves And Kinematical Conservation Laws
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Author : Phoolan Prasad
language : en
Publisher: Springer
Release Date : 2018-03-06
Propagation Of Multidimensional Nonlinear Waves And Kinematical Conservation Laws written by Phoolan Prasad and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-06 with Mathematics categories.
This book formulates the kinematical conservation laws (KCL), analyses them and presents their applications to various problems in physics. Finally, it addresses one of the most challenging problems in fluid dynamics: finding successive positions of a curved shock front. The topics discussed are the outcome of collaborative work that was carried out mainly at the Indian Institute of Science, Bengaluru, India. The theory presented in the book is supported by referring to extensive numerical results. The book is organised into ten chapters. Chapters 1–4 offer a summary of and briefly discuss the theory of hyperbolic partial differential equations and conservation laws. Formulation of equations of a weakly nonlinear wavefront and those of a shock front are briefly explained in Chapter 5, while Chapter 6 addresses KCL theory in space of arbitrary dimensions. The remaining chapters examine various analyses and applications of KCL equations ending in the ultimate goal-propagation of a three-dimensional curved shock front and formation, propagation and interaction of kink lines on it.
Nonlinear Hyperbolic Waves In Multidimensions
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Author : Phoolan Prasad
language : en
Publisher: CRC Press
Release Date : 2001-05-18
Nonlinear Hyperbolic Waves In Multidimensions written by Phoolan Prasad and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-05-18 with Mathematics categories.
The propagation of curved, nonlinear wavefronts and shock fronts are very complex phenomena. Since the 1993 publication of his work Propagation of a Curved Shock and Nonlinear Ray Theory, author Phoolan Prasad and his research group have made significant advances in the underlying theory of these phenomena. This volume presents their results and pr
Nonlinear Wave Equations
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Author : Satyanad Kichenassamy
language : en
Publisher: CRC Press
Release Date : 1995-09-05
Nonlinear Wave Equations written by Satyanad Kichenassamy and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-09-05 with Science categories.
This work examines the mathematical aspects of nonlinear wave propagation, emphasizing nonlinear hyperbolic problems. It introduces the tools that are most effective for exploring the problems of local and global existence, singularity formation, and large-time behaviour of solutions, and for the study of perturbation methods.
Recent Mathematical Methods In Nonlinear Wave Propagation
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Author : Guy Boillat
language : en
Publisher: Springer
Release Date : 2006-11-14
Recent Mathematical Methods In Nonlinear Wave Propagation written by Guy Boillat and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
These lecture notes of the courses presented at the first CIME session 1994 by leading scientists present the state of the art in recent mathematical methods in Nonlinear Wave Propagation.
Mathematical Problems Of Nonlinear Wave Propagation And Of Waves In Heterogeneous Media
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Author : Joseph B. Keller
language : en
Publisher:
Release Date : 1988
Mathematical Problems Of Nonlinear Wave Propagation And Of Waves In Heterogeneous Media written by Joseph B. Keller and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with categories.
The asymptotic behavior of weakly nonlinear waves at caustics is determined for nonlinear wave propagation. A theory is developed for the propagation of short waves of any strength. A method is found for analyzing the stability of a large class of nonlinear waves. The theory of acoustoelasticity is reduced by considering nonlinear effects on waves in granular material. The theory of waves in heterogeneous media analyzed scattering by slender bodies. The pass and stop bands are determined for waves in stratified periodic media. The same is done for an acoustic medium containing rigid spheres arranged in a simple cubic lattice. The amplitude equations are determine for resonantly-interacting water waves in water of nonuniform depth. Keywords: Nonlinear waves; Heterogenous media; Reciprocal theorems; Effective parameters; Pouring flows; Surface flow; Weir flow; Caustics of nonlinear waves; Asymptotic behavior of stability regions for Hill's equation; Stability of periodic plane waves; Lower bounds of permeability; Newtons second law; Stability of plane wave solutions of nonlinear systems; Resonantly interacting water waves; Nonlinear hyperbolic waves. (jhd).