Author: Marcelo Anile
Publisher: CRC Press
ISBN: 1000444856
Category : Mathematics
Languages : en
Pages : 255
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Book Description
Presents in a systematic and unified manner the ray method, in its various forms, for studying nonlinear wave propagation in situations of physical interest, essentially fluid dynamics and plasma physics.
Author: Marcelo Anile
Publisher: Chapman and Hall/CRC
ISBN: 9780582023437
Category : Mathematics
Languages : en
Pages : 264
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Book Description
Presents in a systematic and unified manner the ray method, in its various forms, for studying nonlinear wave propagation in situations of physical interest, essentially fluid dynamics and plasma physics.
Author: Marcelo Anile
Publisher: CRC Press
ISBN: 1000447588
Category : Mathematics
Languages : en
Pages : 268
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Book Description
Presents in a systematic and unified manner the ray method, in its various forms, for studying nonlinear wave propagation in situations of physical interest, essentially fluid dynamics and plasma physics.
Author: I D Iliev
Publisher: CRC Press
ISBN: 9780582239630
Category : Mathematics
Languages : en
Pages : 412
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Book Description
Soliton theory as a method for solving some classes of nonlinear evolution equations (soliton equations) is one of the most actively developing topics in mathematical physics. This book presents some spectral theory methods for the investigation of soliton equations ad the inverse scattering problems related to these equations. The authors give the theory of expansions for the Sturm-Liouville operator and the Dirac operator. On this basis, the spectral theory of recursion operators generating Korteweg-de Vries type equations is presented and the Ablowitz-Kaup-Newell-Segur scheme, through which the inverse scattering method could be understood as a Fourier-type transformation, is considered. Following these ideas, the authors investigate some of the questions related to inverse spectral problems, i.e. uniqueness theorems, construction of explicit solutions and approximative methods for solving inverse scattering problems. A rigorous investigation of the stability of soliton solutions including solitary waves for equations which do not allow integration within inverse scattering method is also presented.
Author:
Publisher:
ISBN:
Category : Nonlinear waves
Languages : en
Pages : 243
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Book Description
Author: Anatoli? Mikha?lovich Kamchatnov
Publisher: World Scientific
ISBN: 981024407X
Category : Science
Languages : en
Pages : 399
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Book Description
Although the mathematical theory of nonlinear waves and solitons has made great progress, its applications to concrete physical problems are rather poor, especially when compared with the classical theory of linear dispersive waves and nonlinear fluid motion. The Whitham method, which describes the combining action of the dispersive and nonlinear effects as modulations of periodic waves, is not widely used by applied mathematicians and physicists, though it provides a direct and natural way to treat various problems in nonlinear wave theory. Therefore it is topical to describe recent developments of the Whitham theory in a clear and simple form suitable for applications in various branches of physics.This book develops the techniques of the theory of nonlinear periodic waves at elementary level and in great pedagogical detail. It provides an introduction to a Whitham's theory of modulation in a form suitable for applications. The exposition is based on a thorough analysis of representative examples taken from fluid mechanics, nonlinear optics and plasma physics rather than on the formulation and study of a mathematical theory. Much attention is paid to physical motivations of the mathematical methods developed in the book. The main applications considered include the theory of collisionless shock waves in dispersive systems and the nonlinear theory of soliton formation in modulationally unstable systems. Exercises are provided to amplify the discussion of important topics such as singular perturbation theory, Riemann invariants, the finite gap integration method, and Whitham equations and their solutions.
Author: Yuri S. Kivshar
Publisher: Academic Press
ISBN: 0080538096
Category : Technology & Engineering
Languages : en
Pages : 557
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Book Description
The current research into solitons and their use in fiber optic communications is very important to the future of communications. Since the advent of computer networking and high speed data transmission technology people have been striving to develop faster and more reliable communications media. Optical pulses tend to broaden over relatively short distances due to dispersion, but solitons on the other hand are not as susceptible to the effects of dispersion, and although they are subject to losses due to attenuation they can be amplified without being received and re-transmitted.This book is the first to provide a thorough overview of optical solitons. The main purpose of this book is to present the rapidly developing field of Spatial Optical Solitons starting from the basic concepts of light self-focusing and self-trapping. It will introduce the fundamental concepts of the theory of nonlinear waves and solitons in non-integrated but physically realistic models of nonlinear optics including their stability and dynamics. Also, it will summarize a number of important experimental verification of the basic theoretical predictions and concepts covering the observation of self-focusing in the earlier days of nonlinear optics and the most recent experimental results on spatial solitons, vortex solitons, and soliton interaction & spiraling.* Introduces the fundamental concepts of the theory of nonlinear waves and solitons through realistic models * Material is based on authors' years of experience actively working in and researching the field* Summarizes the most important experimental verification of the basic theories, predictions and concepts of this ever evolving field from the earliest studies to the most recent
Author: Xing Cai
Publisher: Springer Science & Business Media
ISBN: 3540753834
Category : Science
Languages : en
Pages : 225
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Book Description
In this rapidly evolving world of knowledge and technology, do you ever wonder how hydrology is catching up? Here, two highly qualified scientists edit a volume that takes the angle of computational hydrology and envision one of the science’s future directions – namely, the quantitative integration of high-quality hydrologic field data with geologic, hydrologic, chemical, atmospheric, and biological information to characterize and predict natural systems in hydrological sciences.
Author:
Publisher:
ISBN:
Category : Mathematical physics
Languages : en
Pages : 824
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Book Description
Focuses on fundamental mathematical and computational methods underpinning physics. Relevant to statistical physics, chaotic and complex systems, classical and quantum mechanics, classical and quantum integrable systems and classical and quantum field theory.
Author: Donald Wyman Vasco
Publisher: Cambridge University Press
ISBN: 1316577945
Category : Science
Languages : en
Pages : 381
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Book Description
This book introduces methodologies for subsurface imaging based upon asymptotic and trajectory-based methods for modeling fluid flow, transport and deformation. It describes trajectory-based imaging from its mathematical formulation, through the construction and solution of the imaging equations, to the assessment of the accuracy and resolution associated with the image. Unique in its approach, it provides a unified framework for the complete spectrum of physical phenomena from wave-like hyperbolic problems to diffusive parabolic problems and non-linear problems of mixed character. The practical aspects of imaging, particularly efficient and robust methods for updating high resolution geologic models using fluid flow, transport and geophysical data, are emphasized throughout the book. Complete with online software applications and examples that enable readers to gain hands-on experience, this volume is an invaluable resource for graduate-level courses, as well as for academic researchers and industry practitioners in the fields of geoscience, hydrology, and petroleum and environmental engineering.
