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Methods of Inverse Problems in Physics
This interesting volume focuses on the second of the two broad categories into which problems of physical sciences fall-direct (or forward) and inverse (or backward) problems. It emphasizes one-dimensional problems because of their mathematical clarity. The unique feature of the monograph is its rigorous presentation of inverse problems (from quantum scattering to vibrational systems), transmission lines, and imaging sciences in a single volume. It includes exhaustive discussions on spectral function, inverse scattering integral equations of Gel'fand-Levitan and Marcenko, Povzner-Levitan and Levin transforms, Møller wave operators and Krein's functionals, S-matrix and scattering data, and i...
Mathematics and the 21st Century
The Conference on "Mathematics and the 21st Century" was held in Cairo, Egypt during the period 15-20 January 2000. The conference's sessions consisted of plenary lectures and topical sessions. Some of the plenary lectures covered general fields such as: rewriting the history of mathematics; education of mathematics; relation between mathematics and sciences; and mathematical aspects of transportation.
Solitons and Condensed Matter Physics
Nonl inear ideas of a "sol iton" variety have been a unifying influence on the na tura 1 sci ences for many decades. HO~/ever, thei r uni versa 1 a pprec i at i on in the physics community as a genuine paradigm is very much a current develop ment. All of us who have been associated with this recent wave of enthusiasm were impressed with the variety of applications, their inevitability once the mental contraint of linear normal modes is removed, and above all by the common mathematical structures underpinning applications with quite different (and often novel) physical manifestations. This has certainly been the situ ation in condensed matter, and when, during the Paris Lattice Dynamics Con f...
Order and Chaos in Nonlinear Physical Systems
This volume is concerned with the theoretical description of patterns and instabilities and their relevance to physics, chemistry, and biology. More specifically, the theme of the work is the theory of nonlinear physical systems with emphasis on the mechanisms leading to the appearance of regular patterns of ordered behavior and chaotic patterns of stochastic behavior. The aim is to present basic concepts and current problems from a variety of points of view. In spite of the emphasis on concepts, some effort has been made to bring together experimental observations and theoretical mechanisms to provide a basic understanding of the aspects of the behavior of nonlinear systems which have a mea...
Nonlinear Waves
The outcome of a conference held in East Carolina University in June 1982, this book provides an account of developments in the theory and application of nonlinear waves in both fluids and plasmas. Twenty-two contributors from eight countries here cover all the main fields of research, including nonlinear water waves, K-dV equations, solitions and inverse scattering transforms, stability of solitary waves, resonant wave interactions, nonlinear evolution equations, nonlinear wave phenomena in plasmas, recurrence phenomena in nonlinear wave systems, and the structure and dynamics of envelope solitions in plasmas.
Integrable Hamiltonian Hierarchies
This book presents a detailed derivation of the spectral properties of the Recursion Operators allowing one to derive all the fundamental properties of the soliton equations and to study their hierarchies.
KdV ’95
Exactly one hundred years ago, in 1895, G. de Vries, under the supervision of D. J. Korteweg, defended his thesis on what is now known as the Korteweg-de Vries Equation. They published a joint paper in 1895 in the Philosophical Magazine, entitled `On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary wave', and, for the next 60 years or so, no other relevant work seemed to have been done. In the 1960s, however, research on this and related equations exploded. There are now some 3100 papers in mathematics and physics that contain a mention of the phrase `Korteweg-de Vries equation' in their title or abstract, and there are thousands more in...
Nonlinear Equations in Physics and Mathematics
This is the third Volume in a series of books devoted to the interdisciplinary area between mathematics and physics, all ema nating from the Advanced Study Institutes held in Istanbul in 1970, 1972 and 1977. We believe that physics and mathematics can develop best in harmony and in close communication and cooper ation with each other and are sometimes inseparable. With this goal in mind we tried to bring mathematicians and physicists together to talk and lecture to each other-this time in the area of nonlinear equations. The recent progress and surge of interest in nonlinear ordi nary and partial differential equations has been impressive. At the same time, novel and interesting physical app...
Spectral Transform and Solitons
Spectral Transform and Solitons
Waveguide Propagation of Nonlinear Waves
This book addresses the peculiarities of nonlinear wave propagation in waveguides and explains how the stratification depends on the waveguide and confinement. An example of this is an optical fibre that does not allow light to pass through a density jump. The book also discusses propagation in the nonlinear regime, which is characterized by a specific waveform and amplitude, to demonstrate so-called solitonic behaviour. In this case, a wave may be strongly localized, and propagates with a weak change in shape. In the waveguide case there are additional contributions of dispersion originating from boundary or asymptotic conditions. Offering concrete guidance on solving application problems, ...
