This volume is an introduction to nonlinear waves and soliton theory in the special environment of compact spaces such a closed curves and surfaces and other domain contours. It assumes familiarity with basic soliton theory and nonlinear dynamical systems. The first part of the book introduces the mathematical concept required for treating the manifolds considered, providing relevant notions from topology and differential geometry. An introduction to the theory of motion of curves and surfaces - as part of the emerging field of contour dynamics - is given. The second and third parts discuss the modeling of various physical solitons on compact systems, such as filaments, loops and drops made of almost incompressible materials thereby intersecting with a large number of physical disciplines from hydrodynamics to compact object astrophysics. This book is intended for graduate students and researchers in mathematics, physics and engineering. This new edition has been thoroughly revised, expanded and updated.

The second edition of a highly successful book on nonlinear waves, solitons and chaos.

Travelling wave processes and wave motion are of great importance in many areas of mechanics, and nonlinearity also plays a decisive role there. The basic mathematical models in this area involve nonlinear partial differential equations, and predictability of behaviour of wave phenomena is of great importance. Beside fluid dynamics and gas dynamics, which have long been the traditional nonlinear scienes, solid mechanics is now taking an ever increasing account of nonlinear effects. Apart from plasticity and fracture mechanics, nonlinear elastic waves have been shown to be of great importance in many areas, such as the study of impact, nondestructive testing and seismology. These lectures offer a thorough account of the fundamental theory of nonlinear deformation waves, and in the process offer an up to date account of the current state of research in the theory and practice of nonlinear waves in solids.

Encouraged by the friendly reception given to the first edition, I have preserved its basic form and most of the details. Apart from some corrections, minor changes, and addition of references where it was necessary, I have made the following changes. Chapter 1 was expanded by a discussion of the discovery of soli tons in the field of electromagnetic waves and optics. A new section devoted to nonlinear transmission lines and their applications in the microwave range has been added to Chap. 3. It seems to me that it was important to describe laboratory experiments on modulational instability, and subsequent generation of solitons, both in electrical transmission lines and in deep water in Chaps. 4 and 5. A description of a very simple experimental pocket version of the mechanical transmission line has been included in Chap. 6. Such a versatile and useful device should stimulate a practical approach to soli ton physics. Chapter 7 was completed by a short presentation of some recent experimental results on discrete Josephson transmission lines. A discussion of the experimental modulational instability of coupled optical waves and a simple look at quantum solitons were added to Chap. 8 in order to introduce the reader to such remarkable topics. Of the many people who made valuable comments on the first edition, I am particularly grateful to M. Dragoman, Y. S. Kivshar and A. W. Snyder. I would like to thank R. S. MacKay whose corrections and suggestions helped refine the manuscript of this second edition.

Written for an interdisciplinary readership, this book is a practical guide to the fascinating world of solitons. The author approaches the subject from the standpoint of applications in optics, hydrodynamics, and electrical and chemical engineering. This third edition has been thoroughly revised and updated.

This book addresses the fascinating phenomena associated with nonlinear waves and spatio-temporal patterns. These appear almost everywhere in nature from sand bed forms to brain patterns, and yet their understanding still presents fundamental scientific challenges. The reader will learn here, in particular, about the current state-of-the art and new results in: Nonlinear water waves: resonance, solitons, focusing, Bose-Einstein condensation, as well as and their relevance for the sea environment (sea-wind interaction, sand bed forms, fiber clustering) Pattern formation in non-equilibrium media: soap films, chimera patterns in oscillating media, viscoelastic Couette-Taylor flow, flow in the wake behind a heated cylinder, other pattern formation. The editors and authors dedicate this book to the memory of Alexander Ezersky, Professor of Fluid Mechanics at the University of Caen Normandie (France) from September 2007 to July 2016. Before 2007, he had served as a Senior Scientist at the Institute of Applied Physics of the Russian Academy of Sciences in Nizhny Novgorod (Russia). The chapters have been written by leading scientists in Nonlinear Physics, and the topics chosen so as to cover all the fields to which Prof. Ezersky himself contributed, by means of experimental, theoretical and numerical approaches. The volume will appeal to advanced students and researchers studying nonlinear waves and pattern dynamics, as well as other scientists interested in their applications in various natural media.

Proceedings of a NATO ASI held in Erice, Sicily, Italy, July 1--15, 1989