Rogue and Shock Waves in Nonlinear Dispersive Media


Book Description

This self-contained set of lectures addresses a gap in the literature by providing a systematic link between the theoretical foundations of the subject matter and cutting-edge applications in both geophysical fluid dynamics and nonlinear optics. Rogue and shock waves are phenomena that may occur in the propagation of waves in any nonlinear dispersive medium. Accordingly, they have been observed in disparate settings – as ocean waves, in nonlinear optics, in Bose-Einstein condensates, and in plasmas. Rogue and dispersive shock waves are both characterized by the development of extremes: for the former, the wave amplitude becomes unusually large, while for the latter, gradients reach extreme values. Both aspects strongly influence the statistical properties of the wave propagation and are thus considered together here in terms of their underlying theoretical treatment. This book offers a self-contained graduate-level text intended as both an introduction and reference guide for a new generation of scientists working on rogue and shock wave phenomena across a broad range of fields in applied physics and geophysics.




Nonlinear Dispersive Waves


Book Description




Nonlinear Systems and Their Remarkable Mathematical Structures


Book Description

The third volume in this sequence of books consists of a collection of contributions that aims to describe the recent progress in nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete). Nonlinear Systems and Their Remarkable Mathematical Structures: Volume 3, Contributions from China just like the first two volumes, consists of contributions by world-leading experts in the subject of nonlinear systems, but in this instance only featuring contributions by leading Chinese scientists who also work in China (in some cases in collaboration with western scientists). Features Clearly illustrate the mathematical theories of nonlinear systems and its progress to both the non-expert and active researchers in this area Suitable for graduate students in Mathematics, Applied Mathematics and some of the Engineering sciences Written in a careful pedagogical manner by those experts who have been involved in the research themselves, and each contribution is reasonably self-contained




Guided-Wave Optics


Book Description

This book is a printed edition of the Special Issue "Guided-Wave Optics" that was published in Applied Sciences




Advances in Nonlinear Photonics


Book Description

Advances in Nonlinear Photonics combines fundamental principles with an overview of the latest developments. The book is suitable for the multidisciplinary audience of photonics researchers and practitioners in academia and R&D, including materials scientists and engineers, applied physicists, chemists, etc. As nonlinear phenomena are at the core of photonic devices and may enable future applications such as all-optical switching, all-optical signal processing and quantum photonics, this book provides an overview of key concepts. In addition, the book reviews the most important advances in the field and how nonlinear processes may be exploited in different photonic applications. - Introduces fundamental principles of nonlinear phenomena and their application in materials and devices - Reviews and provides definitions of the latest research directions in the field of nonlinear photonics - Discusses the most important developments in materials and applications, including future prospects




Recent Developments in Integrable Systems and Related Topics of Mathematical Physics


Book Description

This volume, whose contributors include leading researchers in their field, covers a wide range of topics surrounding Integrable Systems, from theoretical developments to applications. Comprising a unique collection of research articles and surveys, the book aims to serve as a bridge between the various areas of Mathematics related to Integrable Systems and Mathematical Physics. Recommended for postgraduate students and early career researchers who aim to acquire knowledge in this area in preparation for further research, this book is also suitable for established researchers aiming to get up to speed with recent developments in the area, and may very well be used as a guide for further study.




Ocean Wave Dynamics


Book Description

Ocean Wave Dynamics is the most up-to-date book of its kind on the three main processes responsible for the generation and evolution of ocean waves: (i) atmospheric input from the wind, (ii) wave breaking and (iii) nonlinear interactions.Ocean waves are important for many reasons. They are the major environmental impact on in the design of coastal or offshore structures. Ocean waves are also fundamental to the processes of coastal flooding and beach erosion. They will play a major role in storm related coastal flooding which will rise in frequency as a result of sea level rise. Ocean waves are also an important part of the coupled ocean-atmosphere system. They determine the roughness of the ocean surface and hence have an impact on winds, fluxes of energy, gases and heat to the ocean and even the stability of ice sheets.Containing the latest research on ocean waves, it is a valuable resource for an overview of knowledge in this important field.Related Link(s)







Unstable Nature


Book Description

Unstable Nature is a popular science book offering a journey through the concept of instability in modern science with a focus on physics. Conceived for the curious reader wishing to go deeper in the fascinating and not yet popularised world of instabilities, it provides an immersion into paradoxical and unexpected phenomena - some of which hides in plain sight in our daily lives. The book is written without technical jargon, and new concepts and terminology needed for the narrative are introduced gradually based on examples taken from accessible everyday life. The chapters are connected through a path that starts from exploring instabilities at the planetary scale and then passes through a description of unstable dynamics in macroscopic settings such as in human mechanical artifacts, fluid waves, animal skin, vegetation structures, and chemical reactions, finally reaching the sub atomic scale and the biological processes of human thought. Before concluding with some general philosophical remarks, a modern landscape about the possibility of seeing instabilities not only as a detrimental effect but as resources to be harnessed for technology is explored. The book is enriched by a variety of professional anecdotes stemming from the direct research experience of the author. It features numerous connections of scientific concepts presented with other branches of the human experience and knowledge including philosophy, engineering, history of science, biology, chemistry, mathematics and computer science, poetry, and meditation. Key Features: Presents an exciting introduction to the topic, which is accessible to those without a scientific background Explores milestone discoveries in the history of the concept of instability in physics Contains anecdotes of key figures from the field, including James C. Maxwell, Alan Turing, Vladimir Zakharov, Edward Lorenz, Enrico Fermi, and Mary Tsingou




Applications of Nonlinear Analysis


Book Description

New applications, research, and fundamental theories in nonlinear analysis are presented in this book. Each chapter provides a unique insight into a large domain of research focusing on functional equations, stability theory, approximation theory, inequalities, nonlinear functional analysis, and calculus of variations with applications to optimization theory. Topics include: Fixed point theory Fixed-circle theory Coupled fixed points Nonlinear duality in Banach spaces Jensen's integral inequality and applications Nonlinear differential equations Nonlinear integro-differential equations Quasiconvexity, Stability of a Cauchy-Jensen additive mapping Generalizations of metric spaces Hilbert-type integral inequality, Solitons Quadratic functional equations in fuzzy Banach spaces Asymptotic orbits in Hill’sproblem Time-domain electromagnetics Inertial Mann algorithms Mathematical modelling Robotics Graduate students and researchers will find this book helpful in comprehending current applications and developments in mathematical analysis. Research scientists and engineers studying essential modern methods and techniques to solve a variety of problems will find this book a valuable source filled with examples that illustrate concepts.