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.

"Mathematical Theory of Dispersion-Managed Optical Solitons" discusses recent advances covering optical solitons, soliton perturbation, optical cross-talk, Gabitov-Turitsyn Equations, quasi-linear pulses, and higher order Gabitov-Turitsyn Equations. Focusing on a mathematical perspective, the book bridges the gap between concepts in engineering and mathematics, and gives an outlook to many new topics for further research. The book is intended for researchers and graduate students in applied mathematics, physics and engineering and also it will be of interest to those who are conducting research in nonlinear fiber optics. Dr. Anjan Biswas is an Associate Professor at the Department of Applied Mathematics & Theoretical Physics, Delaware State University, Dover, DE, USA; Dr. Daniela Milovic is an Associate Professor at the Department of Telecommunications, Faculty of Electronic Engineering, University of Nis, Serbia; Dr. Matthew Edwards is the Dean of the School of Arts and Sciences at Alabama A & M University in Huntsville, AL, USA.

This book provides a historical account of the discovery in 1834 of a remarkable singular wave that was ultimately to lead to the development of modern soliton theory with its diverse physical applications. In terms of associated geometry, the classical work of Bäcklund and Bianchi and its consequences is recounted, notably with regard to nonlinear superposition principles, which later were shown to be generic to soliton systems and which provide the analytic description of complex multi-soliton interaction. Whereas the applications of modern soliton in certain areas of physics are well-documented, deep connections between soliton theory and nonlinear continuum mechanics have had a separate development. This book describes wide applications in such disparate areas as elastostatics, elastodynamics, superelasticity, shell theory, magnetohydrostatics and magnetohydrodynamics, and will appeal to research scientists and advanced students with an interest in integrable systems in nonlinear physics or continuum mechanics.

Numerical Simulations of Physical and Engineering Process is an edited book divided into two parts. Part I devoted to Physical Processes contains 14 chapters, whereas Part II titled Engineering Processes has 13 contributions. The book handles the recent research devoted to numerical simulations of physical and engineering systems. It can be treated as a bridge linking various numerical approaches of two closely inter-related branches of science, i.e. physics and engineering. Since the numerical simulations play a key role in both theoretical and application oriented research, professional reference books are highly needed by pure research scientists, applied mathematicians, engineers as well post-graduate students. In other words, it is expected that the book will serve as an effective tool in training the mentioned groups of researchers and beyond.

In the fourty-seven years that have gone by since the first volume of Progress in Optics was published, optics has become one of the most dynamic fields of science. The volumes in this series which have appeared up to now contain more than 300 review articles by distinguished research workers, which have become permanent records for many important developments. - Backscattering and Anderson localization of light - Advances in oliton manipulation in optical lattices - Fundamental quantum noise in optical amplification - Invisibility cloaks

The contents of the book cover topics on vortex dynamics in a variety of flow problems and describe observational measurements and their interpretation. The book contains 13 chapters that first include vortices in the earth and planetary sciences related to vortices in the Venus plasma wake and also on tropical cyclones and on rotating shallow water in the earth's atmosphere. Vortices in fluid problems include airplane wake vortices, vorticity evolution in free-shear flows, together with axisymmetric flows with swirl, as well as thermal conductivities in fluid layers. Vortices in relativistic fluids, in magnetic disks, solitons and vortices, and relaxation for point vortices were also examined. Other chapters describe conditions in a vortex bioreactor and in vortex yarn structures.

This book highlights the methods to engineer dissipative and magnetic nonlinear waves propagating in nonlinear systems. In the first part of the book, the authors present methodologically mathematical models of nonlinear waves propagating in one- and two-dimensional nonlinear transmission networks without/with dissipative elements. Based on these models, the authors investigate the generation and the transmission of nonlinear modulated waves, in general, and solitary waves, in particular, in networks under consideration. In the second part of the book, the authors develop basic theoretical results for the dynamics matter-wave and magnetic-wave solitons of nonlinear systems and of Bose–Einstein condensates trapped in external potentials, combined with the time-modulated nonlinearity. The models treated here are based on one-, two-, and three-component non-autonomous Gross–Pitaevskii equations. Based on the Heisenberg model of spin–spin interactions, the authors also investigate the dynamics of magnetization in ferromagnet with or without spin-transfer torque. This research book is suitable for physicists, mathematicians, engineers, and graduate students in physics, mathematics, and network and information engineering.