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Author: Roger K. Dodd
Publisher:
ISBN: 9780122191220
Category : Science
Languages : en
Pages : 630
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Book Description
Author: Roger K. Dodd
Publisher:
ISBN: 9780122191220
Category : Science
Languages : en
Pages : 630
Get Book Here
Book Description
Author: Eryk Infeld
Publisher: Cambridge University Press
ISBN: 9780521635578
Category : Mathematics
Languages : en
Pages : 416
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Book Description
The second edition of a highly successful book on nonlinear waves, solitons and chaos.
Author: A.S. Fokas
Publisher: Springer Science & Business Media
ISBN: 3642580459
Category : Science
Languages : en
Pages : 563
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Book Description
In the last ten to fifteen years there have been many important developments in the theory of integrable equations. This period is marked in particular by the strong impact of soliton theory in many diverse areas of mathematics and physics; for example, algebraic geometry (the solution of the Schottky problem), group theory (the discovery of quantum groups), topology (the connection of Jones polynomials with integrable models), and quantum gravity (the connection of the KdV with matrix models). This is the first book to present a comprehensive overview of these developments. Numbered among the authors are many of the most prominent researchers in the field.
Author: Jianke Yang
Publisher: SIAM
ISBN: 0898717051
Category : Science
Languages : en
Pages : 452
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Book Description
Nonlinear Waves in Integrable and Nonintegrable Systems presents cutting-edge developments in the theory and experiments of nonlinear waves. Its comprehensive coverage of analytical and numerical methods for nonintegrable systems is the first of its kind. This book is intended for researchers and graduate students working in applied mathematics and various physical subjects where nonlinear wave phenomena arise (such as nonlinear optics, Bose-Einstein condensates, and fluid dynamics).
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: M. Toda
Publisher: Springer Science & Business Media
ISBN: 9780792304425
Category : Mathematics
Languages : en
Pages : 396
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Book Description
' it is certainly a beautiful presentation, very well adapted to teaching beginners. I am sure this book will be successful.' Inverse Problems, 1990
Author: Mark J. Ablowitz
Publisher: Cambridge University Press
ISBN: 1139503480
Category : Mathematics
Languages : en
Pages : 363
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Book Description
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.
Author: Abdul-Majid Wazwaz
Publisher: Springer Science & Business Media
ISBN: 364200251X
Category : Mathematics
Languages : en
Pages : 746
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Book Description
"Partial Differential Equations and Solitary Waves Theory" is a self-contained book divided into two parts: Part I is a coherent survey bringing together newly developed methods for solving PDEs. While some traditional techniques are presented, this part does not require thorough understanding of abstract theories or compact concepts. Well-selected worked examples and exercises shall guide the reader through the text. Part II provides an extensive exposition of the solitary waves theory. This part handles nonlinear evolution equations by methods such as Hirota’s bilinear method or the tanh-coth method. A self-contained treatment is presented to discuss complete integrability of a wide class of nonlinear equations. This part presents in an accessible manner a systematic presentation of solitons, multi-soliton solutions, kinks, peakons, cuspons, and compactons. While the whole book can be used as a text for advanced undergraduate and graduate students in applied mathematics, physics and engineering, Part II will be most useful for graduate students and researchers in mathematics, engineering, and other related fields. Dr. Abdul-Majid Wazwaz is a Professor of Mathematics at Saint Xavier University, Chicago, Illinois, USA.
Author: Alan C. Newell
Publisher: SIAM
ISBN: 0898711967
Category : Technology & Engineering
Languages : en
Pages : 259
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Book Description
A discussion of the soliton, focusing on the properties that make it physically ubiquitous and the soliton equation mathematically miraculous.
Author: Mark J. Ablowitz
Publisher: Cambridge University Press
ISBN: 0521387302
Category : Mathematics
Languages : en
Pages : 532
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Book Description
This book will be a valuable addition to the growing literature in the area and essential reading for all researchers in the field of soliton theory.
