Asymptotic Wave Theory
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Asymptotic Wave Theory
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Author : Maurice Roseau
language : en
Publisher: Elsevier
Release Date : 2012-12-02
Asymptotic Wave Theory written by Maurice Roseau and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-02 with Mathematics categories.
Asymptotic Wave Theory investigates the asymptotic behavior of wave representations and presents some typical results borrowed from hydrodynamics and elasticity theory. It describes techniques such as Fourier-Laplace transforms, operational calculus, special functions, and asymptotic methods. It also discusses applications to the wave equation, the elements of scattering matrix theory, problems related to the wave equation, and diffraction. Organized into eight chapters, this volume begins with an overview of the Fourier-Laplace integral, the Mellin transform, and special functions such as the gamma function and the Bessel functions. It then considers wave propagation, with emphasis on representations of plane, cylindrical or spherical waves. It methodically introduces the reader to the reflexion and refraction of a plane wave at the interface between two homogeneous media, the asymptotic expansion of Hankel's functions in the neighborhood of the point at infinity, and the asymptotic behavior of the Laplace transform. The book also examines the method of steepest descent, the asymptotic representation of Hankel's function of large order, and the scattering matrix theory. The remaining chapters focus on problems of flow in open channels, the propagation of elastic waves within a layered spherical body, and some problems in water wave theory. This book is a valuable resource for mechanics and students of applied mathematics and mechanics.
Asymptotic Methods In Nonlinear Wave Theory
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Author : Alan Jeffrey
language : en
Publisher: Pitman Advanced Publishing Program
Release Date : 1982
Asymptotic Methods In Nonlinear Wave Theory written by Alan Jeffrey and has been published by Pitman Advanced Publishing Program this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Science categories.
Asymptotic Methods In Nonlinear Wave Phenomena
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Author : Tommaso Ruggeri
language : en
Publisher: World Scientific
Release Date : 2007
Asymptotic Methods In Nonlinear Wave Phenomena written by Tommaso Ruggeri and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
This book brings together several contributions from leading experts in the field of nonlinear wave propagation. This field, which during the last three decades has seen important breakthroughs from the theoretical point of view, has recently acquired increased relevance due to advances in the technology of fluids e.g. at microscale or nanoscale and the recognition of crucial applications to the understanding of biological phenomena. Nonlinear wave theory requires the use of disparate approaches, including formal and rigorous asymptotic methods, Lie group theory, energy methods, numerical analysis, and bifurcation theory. This book presents a unique blend in which different aspects of the theory are enlightened and several real-life applications are investigated. The book will be a valuable resource for applied scientists interested in some of the most recent advances in the theory and in the applications of wave propagation, shock formation, nonequilibrium thermodynamics and energy methods.
Asymptotic Methods In Nonlinear Wave Theory
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Author : A. Jeffrey
language : en
Publisher: Halsted Press
Release Date : 1986-05-01
Asymptotic Methods In Nonlinear Wave Theory written by A. Jeffrey and has been published by Halsted Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-05-01 with categories.
Asymptotic Methods In Short Wavelength Diffraction Theory
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Author : V. M. Babich
language : en
Publisher: Alpha Science International, Limited
Release Date : 2009
Asymptotic Methods In Short Wavelength Diffraction Theory written by V. M. Babich and has been published by Alpha Science International, Limited this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Asymptotic expansions categories.
Dedicated to modern approaches of a high-frequency technique in diffraction theory, Asymptotic Methods in Short-Wavelength Diffraction Theory outlines a variety of crucial topics. The book considers a multitude of matters, ranging from the ray method to the theory of high-frequency whispering-gallery waves alongside the reviewing and reflecting on recent results from the literature dealing with localized asymptotic solutions and uniform representation of a high-frequency wave-field. The book serves as an exclusive address to experts on electromagnetics, seismology and acoustics as well as to mathematicians interested in modern approaches of mathematical physics.
Wave Asymptotics
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Author : P. A. Martin
language : en
Publisher: Cambridge University Press
Release Date : 1992-05-29
Wave Asymptotics written by P. A. Martin and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-05-29 with Mathematics categories.
This volume contains papers by distinguished researchers in fluid mechanics and asymptotics. The papers collected here outline the development of these topics.
Asymptotic Perturbation Theory Of Waves
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Author : Ostrovsky Lev
language : en
Publisher: World Scientific
Release Date : 2014-09-23
Asymptotic Perturbation Theory Of Waves written by Ostrovsky Lev and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-23 with Juvenile Nonfiction categories.
This book is an introduction to the perturbation theory for linear and nonlinear waves in dispersive and dissipative media. The main focus is on the direct asymptotic method which is based on the asymptotic expansion of the solution in series of one or more small parameters and demanding finiteness of the perturbations; this results in slow variation of the main-order solution. The method, which does not depend on integrability of basic equations, is applied to quasi-harmonic and non-harmonic periodic waves, as well as to localized waves such as solitons, kinks, and autowaves. The basic theoretical ideas are illustrated by many physical examples throughout the book.
Short Wavelength Diffraction Theory
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Author : Vasili M. Babic
language : en
Publisher: Springer
Release Date : 2011-12-08
Short Wavelength Diffraction Theory written by Vasili M. Babic and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-08 with Science categories.
In the study of short-wave diffraction problems, asymptotic methods - the ray method, the parabolic equation method, and its further development as the "etalon" (model) problem method - play an important role. These are the meth ods to be treated in this book. The applications of asymptotic methods in the theory of wave phenomena are still far from being exhausted, and we hope that the techniques set forth here will help in solving a number of problems of interest in acoustics, geophysics, the physics of electromagnetic waves, and perhaps in quantum mechanics. In addition, the book may be of use to the mathematician interested in contemporary problems of mathematical physics. Each chapter has been annotated. These notes give a brief history of the problem and cite references dealing with the content of that particular chapter. The main text mentions only those pUblications that explain a given argument or a specific calculation. In an effort to save work for the reader who is interested in only some of the problems considered in this book, we have included a flow chart indicating the interdependence of chapters and sections.
Nonlinear Dispersive Waves
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Author : Mark J. Ablowitz
language : en
Publisher: Cambridge University Press
Release Date : 2011-09-08
Nonlinear Dispersive Waves written by Mark J. Ablowitz and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-08 with Mathematics categories.
The field of nonlinear dispersive waves has developed enormously since the work of Stokes, Boussinesq and Korteweg–de Vries (KdV) in the nineteenth century. In the 1960s, researchers developed effective asymptotic methods for deriving nonlinear wave equations, such as the KdV equation, governing a broad class of physical phenomena that admit special solutions including those commonly known as solitons. This book describes the underlying approximation techniques and methods for finding solutions to these and other equations. The concepts and methods covered include wave dispersion, asymptotic analysis, perturbation theory, the method of multiple scales, deep and shallow water waves, nonlinear optics including fiber optic communications, mode-locked lasers and dispersion-managed wave phenomena. Most chapters feature exercise sets, making the book suitable for advanced courses or for self-directed learning. Graduate students and researchers will find this an excellent entry to a thriving area at the intersection of applied mathematics, engineering and physical science.
Short Wavelength Diffraction Theory
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Author : Vasili M. Babic
language : en
Publisher: Springer
Release Date : 1991
Short Wavelength Diffraction Theory written by Vasili M. Babic and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Science categories.
In the study of short-wave diffraction problems, asymptotic methods - the ray method, the parabolic equation method, and its further development as the "etalon" (model) problem method - play an important role. These are the meth ods to be treated in this book. The applications of asymptotic methods in the theory of wave phenomena are still far from being exhausted, and we hope that the techniques set forth here will help in solving a number of problems of interest in acoustics, geophysics, the physics of electromagnetic waves, and perhaps in quantum mechanics. In addition, the book may be of use to the mathematician interested in contemporary problems of mathematical physics. Each chapter has been annotated. These notes give a brief history of the problem and cite references dealing with the content of that particular chapter. The main text mentions only those pUblications that explain a given argument or a specific calculation. In an effort to save work for the reader who is interested in only some of the problems considered in this book, we have included a flow chart indicating the interdependence of chapters and sections.