Nonlinearity With Disorder

In the past three decades there has been enormous progress in identifying the essential role that nonlinearity plays in physical systems, including supporting soliton-like solutions and self-trapped sxcitations such as polarons. during the same period, similarly impressive progress has occurred in understanding the effects of disorder in linear quantum problems, especially regarding Anderson localization arising from impurities, random spatial structures, stochastic applied fields, and so forth. These striking consequences of disorder, noise and nonlinearity frequently occur together in physical systems. Yet there have been only limited attempts to develop systematic techniques which can include all of these ingredients, which may reinforce, complement or frustrate each other. This book contains a range of articles which provide important steps toward the goal of systematic understanding and classification of phenomenology. Experts from Australia, Europe, Japan, USA, and the USSR describe both mathematical and numerical techniques - especially from soliton and statistical physics disciplines - and applicaations to a number of important physical systems and devices, including optical and electronic transmission lines, liquid crystals, biophysics and magnetism.

Proceedings of the NATO Advanced Research Workshop, Tashkent, Uzbekistan, 2-6 October 2001

This book addresses the issues of nonlinearity and disorder. It covers mathematical and numerical techniques as well as applications of nonlinearity and disorder. The analysis of continuous and discrete systems is also shown.

ill the past three decades there has been enonnous progress in identifying the es sential role that "nonlinearity" plays in physical systems. Classical nonlinear wave equations can support localized, stable "soliton" solutions, and nonlinearities in quantum systems can lead to self-trapped excitations, such as polarons. Since these nonlinear excitations often dominate the transport and response properties of the systems in which they exist, accurate modeling of their effects is essential to interpreting a wide range of physical phenomena. Further, the dramatic de velopments in "deterministic chaos", including the recognition that even simple nonlinear dynamical systems can produce seemingly random temporal evolution, have similarly demonstrated that an understanding of chaotic dynamics is vital to an accurate interpretation of the behavior of many physical systems. As a conse quence of these two developments, the study of nonlinear phenomena has emerged as a subject in its own right. During these same three decades, similar progress has occurred in understand ing the effects of "disorder". Stimulated by Anderson's pioneering work on "dis ordered" quantum solid state materials, this effort has also grown into a field that now includes a variety of classical and quantum systems and treats "disorder" arising from many sources, including impurities, random spatial structures, and stochastic applied fields. Significantly, these two developments have occurred rather independently, with relatively little overlapping research.

This book is a contemporary overview of selected topics in fiber optics. It focuses on the latest research results on light wave manipulation using nonlinear optical fibers, with the aim of capturing some of the most innovative developments on this topic. The book’s scope covers both fundamentals and applications from both theoretical and experimental perspectives, with topics including linear and nonlinear effects, pulse propagation phenomena and pulse shaping, solitons and rogue waves, novel optical fibers, supercontinuum generation, polarization management, optical signal processing, fiber lasers, optical wave turbulence, light propagation in disordered fiber media, and slow and fast light. With contributions from leading-edge scientists in the field of nonlinear photonics and fiber optics, they offer an overview of the latest advances in their own research area. The listing of recent research papers at the end of each chapter is useful for researchers using the book as a reference. As the book addresses fundamental and practical photonics problems, it will also be of interest to, and benefit, broader academic communities, including areas such as nonlinear science, applied mathematics and physics, and optical engineering. It offers the reader a wide and critical overview of the state-of-the-art within this practical – as well as fundamentally important and interesting – area of modern science, providing a useful reference which will encourage further research and advances in the field.

The Sixth Annual Conference of the Center for Nonlinear Studies at the Los Alamos National Laboratory was held May 5-9, 1986, on the topic "Nonlinearity in Condensed Matter: Lessons from the Past and Prospects for the Future. " As conference organizers, we felt that the study of non linear phenomena in condensed matter had matured to the point where it made sense to take stock of the numerous lessons to be learned from a variety of contexts where nonlinearity plays a fundamental role and to evaluate the prospects for the growth of this general discipline. The successful 1978 Oxford Symposium on nonlinear (soliton) struc ture and dynamics in condensed matter (Springer Ser. Solid-State Sci. , Vol. 8) was held at a time when the ubiquity of solitons was just begin ning to be appreciated by the condensed matter community; in subsequent years the soliton paradigm has provided a rather useful framework for in vestigating a large number of phenomena, particularly in low-dimensional systems. Nevertheless, we felt that the importance of nonlinearity in wider arenas than "solitonics" merited a significant expansion in the scope of the conference over that of the 1978 symposium. Indeed, many of the lessons are quite general and their potential for cross-fertilization of otherwise poorly connected disciplines was certainly one of the prime motivations for this conference. Thus, while these proceedings contain many contribu tions pertaining to soliton behavior in different contexts, the reader will find much more as well, particularly in the later chapters.