Panayotis G. Kevrekidis – författare

Nonlinear waves are of significant scientific interest across many diverse contexts, ranging from mathematics and physics to engineering, biosciences, chemistry, and finance. The study of nonlinear waves is relevant to Bose-Einstein condensates, the interaction of electromagnetic waves with matter, optical fibers and waveguides, acoustics, water waves, atmospheric and planetary scales, and even galaxy formation. The aim of this book is to provide a self-contained introduction to the continuously developing field of nonlinear waves, that offers the background, the basic ideas, and mathematical, as well as computational methods, while also presenting an overview of associated physical applications.Originated from the authors' own research activity in the field for almost three decades and shaped over many years of teaching on relevant courses, the primary purpose of this book is to serve as a textbook. However, the selection and exposition of the material will be useful to anyone who is curious to explore the fascinating world of nonlinear waves.

Nonlinear waves are of significant scientific interest across many diverse contexts, ranging from mathematics and physics to engineering, biosciences, chemistry, and finance. The study of nonlinear waves is relevant to Bose-Einstein condensates, the interaction of electromagnetic waves with matter, optical fibers and waveguides, acoustics, water waves, atmospheric and planetary scales, and even galaxy formation. The aim of this book is to provide a self-contained introduction to the continuously developing field of nonlinear waves, that offers the background, the basic ideas, and mathematical, as well as computational methods, while also presenting an overview of associated physical applications.Originated from the authors' own research activity in the field for almost three decades and shaped over many years of teaching on relevant courses, the primary purpose of this book is to serve as a textbook. However, the selection and exposition of the material will be useful to anyone who is curious to explore the fascinating world of nonlinear waves.

Bose–Einstein condensation is a phase transition in which a fraction of particles of a boson gas condenses into the same quantum state known as the Bose–Einstein condensate (BEC). The aim of this book is to present a wide array of findings in the realm of BECs and on the nonlinear Schrödinger-type models that arise therein.The Defocusing Nonlinear Schrödinger Equation is a broad study of nonlinear excitations in self-defocusing nonlinear media. It summarizes state-of-the-art knowledge on the defocusing nonlinear Schrödinger-type models in a single volume and contains a wealth of resources, including over 800 references to relevant articles and monographs and a meticulous index for ease of navigation.

This book presents a careful selection of the most important developments of the \phi^4 model, offering a judicious summary of this model with a view to future prospects and the challenges ahead.

This book explores the impact of nonlinearity on a broad range of areas, including time-honored fields such as biology, geometry, and topology, but also modern ones such as quantum mechanics, networks, metamaterials and artificial intelligence.

This book explores the role of fractional calculus and associated partial differential equations in modeling multiscale phenomena and overlapping macroscopic & microscopic scales, offering an innovative and powerful tool for modeling complex systems. While integer order PDEs have a long-standing history, the novel setting of fractional PDEs opens up new possibilities for the simulation of multi-physics phenomena. The book examines a range of releavant examples that showcase the seamless transition from wave propagation to diffusion or from local to non-local dynamics in both continuum and discrete systems. These systems have been argued as being particularly relevant in contexts such as nonlinear optics, lattice nonlinear dynamical systems, and dispersive nonlinear wave phenomena, where the exploration of the potential fractionality has emerged as a highly active topic for current studies.The volume consists of contributions from a diverse group of active scholars and expertsacross different fields, providing a detailed examination of the field's past, present, and future state-of-the-art in the interplay of fractional PDEs and nonlinear wave phenomena. It is intended to be of wide interest to both seasoned researchers and beginners in the Field of Nonlinear Science. This book sets the stage for the next decade of research and beyond and is a timely and relevant reference of choice for this crucial junction of current research.

This book explores the role of fractional calculus and associated partial differential equations in modeling multiscale phenomena and overlapping macroscopic & microscopic scales, offering an innovative and powerful tool for modeling complex systems. While integer order PDEs have a long-standing history, the novel setting of fractional PDEs opens up new possibilities for the simulation of multi-physics phenomena. The book examines a range of releavant examples that showcase the seamless transition from wave propagation to diffusion or from local to non-local dynamics in both continuum and discrete systems. These systems have been argued as being particularly relevant in contexts such as nonlinear optics, lattice nonlinear dynamical systems, and dispersive nonlinear wave phenomena, where the exploration of the potential fractionality has emerged as a highly active topic for current studies.The volume consists of contributions from a diverse group of active scholars and expertsacross different fields, providing a detailed examination of the field's past, present, and future state-of-the-art in the interplay of fractional PDEs and nonlinear wave phenomena. It is intended to be of wide interest to both seasoned researchers and beginners in the Field of Nonlinear Science. This book sets the stage for the next decade of research and beyond and is a timely and relevant reference of choice for this crucial junction of current research.

The sine-Gordon model is a ubiquitous model of Mathematical Physics with a wide range of applications extending from coupled torsion pendula and Josephson junction arrays to gravitational and high-energy physics models. The purpose of this book is to present a summary of recent developments in this field, incorporating both introductory background material, but also with a strong view towards modern applications, recent experiments, developments regarding the existence, stability, dynamics and asymptotics of nonlinear waves that arise in the model. This book is of particular interest to a wide range of researchers in this field, but serves as an introductory text for young researchers and students interested in the topic. The book consists of well-selected thematic chapters on diverse mathematical and physical aspects of the equation carefully chosen and assigned.

The sine-Gordon model is a ubiquitous model of Mathematical Physics with a wide range of applications extending from coupled torsion pendula and Josephson junction arrays to gravitational and high-energy physics models. The purpose of this book is to present a summary of recent developments in this field, incorporating both introductory background material, but also with a strong view towards modern applications, recent experiments, developments regarding the existence, stability, dynamics and asymptotics of nonlinear waves that arise in the model. This book is of particular interest to a wide range of researchers in this field, but serves as an introductory text for young researchers and students interested in the topic. The book consists of well-selected thematic chapters on diverse mathematical and physical aspects of the equation carefully chosen and assigned.

This book summarizes a number of fundamental developments at the interface of granular crystals and the mathematical and computational analysis of some of their key localized nonlinear wave solutions. The subject presents a blend of the appeal of granular crystals as a prototypical engineering tested for a variety of diverse applications, the novelty in the nonlinear physics of its coherent structures, and the tractability of a series of mathematical and computational techniques to analyse them. While the focus is on principal one-dimensional solutions such as shock waves, traveling waves, and discrete breathers, numerous extensions of the discussed patterns, e.g., in two dimensions, chains with defects, heterogeneous settings, and other recent developments are discussed. The emphasis on the subject was motivated by models in condensed matter physics, ferroelectrics, high energy physics, and statistical mechanics, leading to developments in mathematical analysis, numerical computation and insights on the physical aspects of the model. The book appeals to researchers in the field, as well as for graduate and advanced undergraduate students. It will be of interest to mathematicians, physicists and engineers alike.

The ?eld of Bose–Einstein condensation in atomic gases has been full of s- prises.Whathappenedafterthe?rstrealization ofBose–Einstein condensates in 1995 has far exceeded the vision of their creators. Originally, I expected interesting studies of equilibrium properties and dynamics, but the Bose– Einstein condensate became a pristine platform for a host of scienti?c studies. The condensate turned out to be a well-controlled medium for nonlinear wave phenomenaincludingfour-wavemixing,darkandbrightsolitons,anddynamic instabilities. Rotating condensates gave access to the rich physics of vortices and vortex lattices. The availability of di?erent hyper?ne states led to mul- component or spinor condensates, and optical lattices opened up yet another major frontier which is still rapidly expanding. Feshbach resonances and c- densation of fermion pairs will provide interesting phenomena to study for many more years to come. This rapid development of the ?eld has been fueled by a unique int- play between experiment and theory. Although experimentalists had the lead in realizing new systems, many phenomena were ?rst predicted and then observed. The present book re?ects this symbiosis by a balance of theoretical and experimental contributions. Twelve years after its beginning, the ?eld has reached a degree of maturity which is much better represented by a comp- hensive book than by a collection of original articles. I therefore expect this book not only to provide a valuable introduction to many young researchers who are joining this ?eld, but also serve as a reference for further studies of nonlinear phenomena in this rich system.

Adventures of nonlinear science were perhaps most notably seeded at the Los Alamos National Laboratory (LANL) over half a century ago with the fundamental questionsofenergyequipartitioninnonlinearsystems, astheywereposedbyFermi, Pasta, and Ulam. At the time, probably little could be imagined of the far-reaching implications that the studies of nonlinear phenomena would have, continuing to expandtothisday.TheGinzburg-Landautheoryofsuperconductivityandtheord- parameter descriptions of super uidity, the "soliton revolution" through the works of Zabusky and Kruskal on the KdV equation and the subsequent widespread - plicationsof the nonlinear Schrodi .. ngerequation in optical bers and Bose-Einstein condensates,the developmentsof bifurcationtheory and chaotic dynamicsand their widespread applicationsfrom climate and geophysics,to biological phenomenaand chemical kineticsare only a few of the multiple arenas in which nonlineardynamics have emerged as the appropriate description of important physical systems.I well remember my own early days of nonlinear science appreciation, rst at Cornell University in the early 1970s and then at Los Alamos where we began the Center for Nonlinear Studies (CNLS) in 1980. These were years marked by interdisciplinary discovery and by the recognition that many nonlinear equations have an inherent ability to exhibit both coherence and chaos - the beginnings of our appreciation today of spatio-temporal complexity and the functional role that this plays in multiple branches of science, technology, and engineering.

The ?eld of Bose–Einstein condensation in atomic gases has been full of s- prises.Whathappenedafterthe?rstrealization ofBose–Einstein condensates in 1995 has far exceeded the vision of their creators. Originally, I expected interesting studies of equilibrium properties and dynamics, but the Bose– Einstein condensate became a pristine platform for a host of scienti?c studies. The condensate turned out to be a well-controlled medium for nonlinear wave phenomenaincludingfour-wavemixing,darkandbrightsolitons,anddynamic instabilities. Rotating condensates gave access to the rich physics of vortices and vortex lattices. The availability of di?erent hyper?ne states led to mul- component or spinor condensates, and optical lattices opened up yet another major frontier which is still rapidly expanding. Feshbach resonances and c- densation of fermion pairs will provide interesting phenomena to study for many more years to come. This rapid development of the ?eld has been fueled by a unique int- play between experiment and theory. Although experimentalists had the lead in realizing new systems, many phenomena were ?rst predicted and then observed. The present book re?ects this symbiosis by a balance of theoretical and experimental contributions. Twelve years after its beginning, the ?eld has reached a degree of maturity which is much better represented by a comp- hensive book than by a collection of original articles. I therefore expect this book not only to provide a valuable introduction to many young researchers who are joining this ?eld, but also serve as a reference for further studies of nonlinear phenomena in this rich system.