There are various types of waves including water, sound, electromagnetic, seismic and shock etc. These waves need to be analyzed and understood for different practical applications. This book is an attempt to consider the waves in detail to understand the physical and mathematical phenomena. A major challenge is to model waves by experimental studies.The aim of this book is to address the efficient and recently developed theories along with the basic equations of wave dynamics. The latest development of analytical/semi analytical and numerical methods with respect to wave dynamics are also covered. Further few challenging experimental studies are considered for related problems. This book presents advances in wave dynamics in simple and easy to follow chapters for the benefit of the readers/researchers.

This monograph is devoted to problems of propagation and stability of linear and nonlinear waves in continuous media with complex structure. It considers the different media, such as solid with cavities, preliminary deformed disperse medium, solid with porosity filled by the electrically conductive and non-conductive liquid, magnetoelastic, piezo-semiconductors, crystals with dislocations, composites with inclusions, an electrically conductive asymmetrical liquid, a mixture of gas with a drop liquid. The book also considers the propagation of a laser beam through a two-level medium. The presented results are based on methods of evolution and modulation equations that were developed by the authors. The book is intended for scientific and technical researchers, students and post-graduate students specializing in mechanics of continuous media, physical acoustics, and physics of the solid state.

At the end of the twentieth century, nonlinear dynamics turned out to be one of the most challenging and stimulating ideas. Notions like bifurcations, attractors, chaos, fractals, etc. have proved to be useful in explaining the world around us, be it natural or artificial. However, much of our everyday understanding is still based on linearity, i. e. on the additivity and the proportionality. The larger the excitation, the larger the response-this seems to be carved in a stone tablet. The real world is not always reacting this way and the additivity is simply lost. The most convenient way to describe such a phenomenon is to use a mathematical term-nonlinearity. The importance of this notion, i. e. the importance of being nonlinear is nowadays more and more accepted not only by the scientific community but also globally. The recent success of nonlinear dynamics is heavily biased towards temporal characterization widely using nonlinear ordinary differential equations. Nonlinear spatio-temporal processes, i. e. nonlinear waves are seemingly much more complicated because they are described by nonlinear partial differential equations. The richness of the world may lead in this case to coherent structures like solitons, kinks, breathers, etc. which have been studied in detail. Their chaotic counterparts, however, are not so explicitly analysed yet. The wavebearing physical systems cover a wide range of phenomena involving physics, solid mechanics, hydrodynamics, biological structures, chemistry, etc.

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.

Waves: Fundamentals and dynamics' discusses the various aspects of wave dynamics from many different perspectives. The main topics include the fundamentals of oscillations and waves, the big picture of wave dynamics as a propagation of oscillation, the mathematical aspects of waves, the various properties of waves, and the propagation of waves along with some actual techniques. Each concept is broken down to be as easily digestible as possible in order to facilitate understanding of the underlying physics.

Waves are everywhere in our daily life. We all experience sound and light with our ears and eyes, we use microwaves to cook, and radio waves are transmitted from and are received by our cell phones. These are just some examples of waves that carry energy from point A to B. However, we may not know details of the physics underlying all these waves. It is important to understand the mechanisms that generate wave dynamics for a given system. It is not straightforward to explain how an electromagnetic field becomes oscillatory and propagates as a wave. Waves sometimes represent the underlying dynamics of observed phenomena at a fundamental level of physics. This book is designed to explore these mechanisms by discussing various aspects of wave dynamics from as many perspectives as possible. The target audiences are undergraduate students majoring in engineering science and graduate students majoring in general engineering. Going beyond the typical approach to learning science, this book discusses wave dynamics and related concepts at various levels of mathematics and physics, sometimes touching on profound physics behind them. This book was written to help readers learn wave dynamics on a deep physical level, and develop innovative ideas in their own fields.