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.

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.

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. Covering 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.

During the past ten years, there has been intensive development in theoretical and experimental research of solitons in periodic media. This book provides a unique and informative account of the state-of-the-art in the field. The volume opens with a review of the existence of robust solitary pulses in systems built as a periodic concatenation of very different elements. Among the most famous examples of this type of systems are the dispersion management in fiber-optic telecommunication links, and (more recently) photonic crystals. A number of other systems belonging to the same broad class of spatially periodic strongly inhomogeneous media (such as the split-step and tandem models) have recently been identified in nonlinear optics, and transmission of solitary pulses in them was investigated in detail. Similar soliton dynamics occurs in temporal-domain counterparts of such systems, where they are subject to strong time-periodic modulation (for instance, the Feshbach-resonance management in Bose-Einstein condensates). Basis results obtained for all these systems are reviewed in the book. This timely work will serve as a useful resource for the soliton community.

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

In mathematics and physics, a soliton is a self-reinforcing solitary wave (a wave packet or pulse) that maintains its shape while it travels at constant speed. Solitons are caused by a cancellation of non-linear and dispersive effects in the medium. In this book, the authors discuss the interactions and theoretical and experimental challenges of solitons. Topics include soliton motion of electrons and its physical properties in coupled electron-phonon systems and ionic crystals; soliton excitations and its experimental evidence in molecular crystals; shapes and dynamics of semi-discrete solitons in arrayed and stacked waveguiding systems; and more.

This book summarizes the proceedings of the invited talks presented at the International Symposium on New Trends in Optical Soliton Transmission Systems held in Kyoto during November 18 - 21, 1997. As a result of worldwide demand for ultra high bitrate transmissions and increased scientific interest from the soliton community, research on optical solitons in fibres has made remarkable progress in recent years. In view of these trends, 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. As with the 1 st ROSC symposium, this symposium attracted enthusiastic response from worldwide researchers involved in the subject of soliton based communications and intensive discussions were held throughout the symposium. Particular emphases were made to dispersion managements of soliton transmission. I would like to note that in the }'t symposium the (adiabatic) dispersion managements just began to appear in reducing radiation at amplifiers and reducing collision effects in WDM system. These have become standard this time, but in addition new, non-adiabatic dispersion managements have been introduced independently by various scientists all over the world.