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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.
Soliton theory is an important branch of applied mathematics and mathematical physics. An active and productive field of research, it has important applications in fluid mechanics, nonlinear optics, classical and quantum fields theories etc. This book presents a broad view of soliton theory. It gives an expository survey of the most basic ideas and methods, such as physical background, inverse scattering, Backlünd transformations, finite-dimensional completely integrable systems, symmetry, Kac-moody algebra, solitons and differential geometry, numerical analysis for nonlinear waves, and gravitational solitons. Besides the essential points of the theory, several applications are sketched and some recent developments, partly by the authors and their collaborators, are presented.
A good deal of the material presented in this book has been prepared by top experts in the field lecturing in January 1987 at the Winter School on Solitons in Tiruchirapalli,India. The lectures begin at an elementary level but go on to include even the most recent developments in the field. The book makes a handy introduction to the various facets of the soliton concept, and will be useful both to newcomers to the field and to researchers who are interested in developments in new branches of physics and mathematics.
Since their discovery a mere thirty years ago, solitons have been invoked to explain such diverse phenomena as: The long lived 'giant red spot' in the highly turbulent Jovian atmosphere. The famous Fermi-Pasta-Ulam paradox wherein a nonlinearly coupled lattice of particles does not display the 'expected equipartition of energy among available modes. It covers: Ion-acoustic waves in a plasma; Energy storage and transfer in proteins via the Davydov soliton; and The propagation of short laser pulses in optical fibres over long distances with negligible shape change. This volume presents important research from around the globe.
This volume is composed of papers (invited and contributed) presented at the International Conference on Coherence and Quantum Optics held at the University of Hyderabad January 5-January 10, 1991. It has been organized by Professor Girish Agarwal and his colleagues at the School of Physics, University of Hyderabad, Hyder abad, India under partial support from the Department of Science and Technology, Government of India, International Center for Theoretical Physics, Trieste, Italy and the National Science Foundation, USA. Without the untiring efforts of Prof. Girish Agarwal and the members of his quantum office group, the Conference and the present volume would not have been possible. Some extraordinary circumstances resulted in a delay of the publication of the present volume. Our sincere apologies to all the authors. We deeply regret the inconvenience caused due to the delay. A debt of gratitude is due to Ms. Kim Bella for the excellent typing job of the different versions and the final version of the manuscript. It is a pleasure to acknowl edge the efforts of Ms. Pat Vann, Mr. Greg Safford and Mr. Eric Katz of the Plenum Publishing, without whose interest and persistence this volume would not have been possible. v CONTENTS QUANTUM OPTICS: THEORY The Quantum Mechanics of Particles in Time-Dependent Quadrupole Fields Roy J. Glauber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Localization of Photons in Random and Quasiperiodic Media S. Dutta Gupta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Enhanced Fundamental Linewidth of a Laser Due to Outcoupling W. A. Hamel, M. P. van Exter, and J. P. Woerdman . . . . . . . . . . . . . . . . . . . . . . . .
Account of method of solving soliton equations by the inventor of the method.
The Marcel Grossmann Meetings are three-yearly forums that meet to discuss recent advances in gravitation, general relativity and relativistic field theories, emphasizing their mathematical foundations, physical predictions and experimental tests. These meetings aim to facilitate the exchange of ideas among scientists, to deepen our understanding of space-time structures, and to review the status of ongoing experiments and observations testing Einstein's theory of gravitation either from ground or space-based experiments. Since the first meeting in 1975 in Trieste, Italy, which was established by Remo Ruffini and Abdus Salam, the range of topics presented at these meetings has gradually widened to accommodate issues of major scientific interest, and attendance has grown to attract more than 900 participants from over 80 countries.This proceedings volume of the eleventh meeting in the series, held in Berlin in 2006, highlights and records the developments and applications of Einstein's theory in diverse areas ranging from fundamental field theories to particle physics, astrophysics and cosmology, made possible by unprecedented technological developments in experimental and observational techniques from space, ground and underground observatories. It provides a broad sampling of the current work in the field, especially relativistic astrophysics, including many reviews by leading figures in the research community.