This volume contains the Proceedings of the NATO Advanced Research Workshop (ARW) and Emil-Warburg-Symposium (EWS) "Nonlinear Coherent Structures in Phy sics and Biology" held at the University of Bayreuth from June 1 -4, 1993. Director of the ARW was K. H. Spatschek, while F.G. Mertens acted as the co-director, host, and organizer of the EWS. The other members of the scientific organizing committee were A.R. Bishop (Los Alamos), J.C. Eilbeck (Edinburgh), and M. Remoissenet (Dijon). This was the eighth meeting in a series of interdisciplinary workshops founded by our French colleagues who had organized all the previous workshops, e.g. 1989 in Montpel lier and 1991 in Dijon. We were asked to organize the meeting this time in Germany. Of course, we wanted to keep the character defined by the previous meetings, which were always characterized by an open and friendly atmosphere, being not too large in quantity, but high in quality. This time altogether 103 participants attended the workshop. During the past years most of the participants met several times and discussed problems connected with the generation of nonlinear coherent structures in physics and biology.

In 438 alphabetically-arranged essays, this work provides a useful overview of the core mathematical background for nonlinear science, as well as its applications to key problems in ecology and biological systems, chemical reaction-diffusion problems, geophysics, economics, electrical and mechanical oscillations in engineering systems, lasers and nonlinear optics, fluid mechanics and turbulence, and condensed matter physics, among others.

This conference was the third meeting organized in the framework of the European LOCNET project. The main topics discussed by this international research collaboration were localization by nonlinearity and spatial discreteness, and energy transfer (in crystals, biomolecules and Josephson arrays).

The NATO Advanced Research Workshop on Coherent Optical Processes in Semiconductors was held in Cambridge, England on August 11-14,1993. The idea of holding this Workshop grew from the recent upsurge in activity on coherent transient effects in semiconductors. The development of this field reflects advances in both light sources and the quality of semiconductor structures, such that tunable optical pulses are now routinely available whose duration is shorter than the dephasing time for excitonic states in quantum wells. It was therefore no surprise to the organisers that as the programme developed, there emerged a heavy emphasis on time-resolved four-wave mixing, particularly in quantum wells. Nevertheless, other issues concerned with coherent effects ensured that several papers on related problems contributed some variety. The topics discussed at the workshop centred on what is a rather new field of study, and benefited enormously by having participants representing many of the principal groups working in this area. Several themes emerged through the invited contributions at the Workshop. One important development has been the careful examination of the two-level model of excitonic effects; a model which has been remarkably successful despite the expected complexities arising from the semiconductor band structure. Indeed, modest extensions to the two level model have been able to offer a useful account for some of the complicated polarisation dependence of four-wave mixing signals from GaAs quantum wells. This work clearly is leading to an improved understanding of excitons in confined systems.

This book summarizes the proceedings of the invited talks presented at the International Symposium of Physics and Application of Optical Solitons in Fibers held in Kyoto during November 14 to 17,1995. As a result of worldwide demand for ultra high bitrate transmissions and increased scientific interests from the soliton community, research on optical solitons in fibers has made a remarkable progress in recent years. In view of these trends, and with the support of the Japanese Ministry of Posts and Telecommunications, the Research Group for Optical Soliton Communications (ROSC), chaired by Akira Hasegawa, was established in Japan in April 1995 to promote collaboration and information exchange 'among communication service companies, industries and academic circles in the theory and application of optical solitons. This symposium was organized as a part of the ROSC activities. The symposium attracted enthusiastic response by worldwide researchers involved in this subject which has lead to the most intensive meeting that the editor ever attended. The reader will find the contents to be well-balanced among theory, experiment and technology. Although the evaluation of the contents shall naturally depend on the particular area of interest of the reader, the symposium has confirmed that the soliton based light wave transmission has achieved the best result in one channel, both in distance of transmission and in bitrate although in wavelength division multiplexed (WDM) systems, NRZ transmission has yet better result.

We have classified the articles presented here in two Sections according to their general content. In Part I we have included papers which deal with statistical mechanics, math ematical aspects of dynamical systems and sthochastic effects in nonequilibrium systems. Part II is devoted mainly to instabilities and self-organization in extended nonequilibrium systems. The study of partial differential equations by numerical and analytic methods plays a great role here and many works are related to this subject. Most recent developments in this fascinating and rapidly growing area are discussed. PART I STATISTICAL MECHANICS AND RELATED TOPICS NONEQUILIBRIUM POTENTIALS FOR PERIOD DOUBLING R. Graham and A. Hamm Fachbereich Physik, Universitiit Gesamthochschule Essen D4300 Essen 1 Germany ABSTRACT. In this lecture we consider the influence of weak stochastic perturbations on period doubling using nonequilibrium potentials, a concept which is explained in section 1 and formulated for the case of maps in section 2. In section 3 nonequilibrium potentials are considered for the family of quadratic maps (a) at the Feigenbaum 'attractor' with Gaussian noise, (b) for more general non Gaussian noise, and (c) for the case of a strange repeller. Our discussion will be informal. A more detailed account of this and related material can be found in our papers [1-3] and in the reviews [4, 5], where further references to related work are also given. 1.

Nonlinear science is by now a well established field of research at the interface of many traditional disciplines and draws on the theoretical concepts developed in physics and mathematics. The present volume gathers the contributions of leading scientists to give the state of the art in many areas strongly influenced by nonlinear research, such as superconduction, optics, lattice dynamics, biology and biomolecular dynamics. While this volume is primarily intended for researchers working in the field care, has been taken that it will also be of benefit to graduate students or nonexpert scientist wishing to familiarize themselves with the current status of research.

This book constitutes the first effort to summarize a large volume of results obtained over the past 20 years in the context of the Discrete Nonlinear Schrödinger equation and the physical settings that it describes.

This book contains the proceedings of an international conference on Numerical Methods for Fluid Dynamics held at the University of Oxford in April 1995. It provides a summary of recent research on the computational aspects of fluid dynamics. It includes contributions from many distinguished mathematicians and engineers and, as always, the standard of papers is high. The main themes of the book are algorithms and algorithmic needs arising from applications, Navier-Stokes on flexible grids, and environmental computational fluid dynamics. Graduate students of numerical analysis will find the up-to-date coverage of research in this book very useful.