Ricardo Carretero-González - Böcker

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.

The study of nonlinear localized excitations is a long-standing challenge for research in basic and applied science, as well as engineering, due to their importance in understanding and predicting phenomena arising in nonlinear and complex systems, but also due to their potential for the development and design of novel applications. This volume is a compilation of chapters representing the current state-of-the-art on the field of localized excitations and their role in the dynamics of complex physical systems.

The study of nonlinear localized excitations is a long-standing challenge for research in basic and applied science, as well as engineering, due to their importance in understanding and predicting phenomena arising in nonlinear and complex systems, but also due to their potential for the development and design of novel applications. This volume is a compilation of chapters representing the current state-of-the-art on the field of localized excitations and their role in the dynamics of complex physical systems.

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.