The Defocusing Nonlinear Schr Dinger Equation
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The Defocusing Nonlinear Schr Dinger Equation
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Author : Panayotis G. Kevrekidis
language : en
Publisher: SIAM
Release Date : 2015-08-04
The Defocusing Nonlinear Schr Dinger Equation written by Panayotis G. Kevrekidis and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-04 with Mathematics categories.
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 SchrÓdinger-type models that arise therein.÷The Defocusing Nonlinear SchrÓdinger Equation÷is a broad study of nonlinear÷excitations in self-defocusing nonlinear media. It summarizes state-of-the-art knowledge on the defocusing nonlinear SchrÓdinger-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.
Defocusing Nonlinear Schr Dinger Equations
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Author : Benjamin Dodson
language : en
Publisher: Cambridge University Press
Release Date : 2019-03-28
Defocusing Nonlinear Schr Dinger Equations written by Benjamin Dodson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-28 with Mathematics categories.
Explores Schrödinger equations with power-type nonlinearity, with scattering results for mass- and energy-critical Schrödinger equations.
The Defocusing Nls Equation And Its Normal Form
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Author :
language : en
Publisher:
Release Date : 2014
The Defocusing Nls Equation And Its Normal Form written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with categories.
The Defocusing Nls Equation And Its Normal Form
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Author : Benoit Grébert
language : en
Publisher: Erich Schmidt Verlag GmbH & Co. KG
Release Date : 2014
The Defocusing Nls Equation And Its Normal Form written by Benoit Grébert and has been published by Erich Schmidt Verlag GmbH & Co. KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Schrödinger equation categories.
The theme of this monograph is the nonlinear Schrodinger equation. This equation models slowly varying wave envelopes in dispersive media and arises in various physical systems such as water waves, plasma physics, solid state physics and nonlinear optics. More specifically, this book treats the defocusing nonlinear Schrodinger (dNLS) equation on the circle with a dynamical systems viewpoint. By developing the normal form theory, it is shown that this equation is an integrable partial differential equation in the strongest possible sense. In particular, all solutions of the dNLS equation on the circle are periodic, quasi-periodic or almost-periodic in time and Hamiltonian perturbations of this equation can be studied near solutions far away from the equilibrium. The book is intended not only for specialists working at the intersection of integrable PDEs and dynamical systems but also for researchers farther away from these fields as well as for graduate students. It is written in a modular fashion; each of its chapters and appendices can be read independently of each other.
Dispersive Equations And Nonlinear Waves
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Author : Herbert Koch
language : en
Publisher: Springer
Release Date : 2014-07-14
Dispersive Equations And Nonlinear Waves written by Herbert Koch and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-14 with Mathematics categories.
The first part of the book provides an introduction to key tools and techniques in dispersive equations: Strichartz estimates, bilinear estimates, modulation and adapted function spaces, with an application to the generalized Korteweg-de Vries equation and the Kadomtsev-Petviashvili equation. The energy-critical nonlinear Schrödinger equation, global solutions to the defocusing problem, and scattering are the focus of the second part. Using this concrete example, it walks the reader through the induction on energy technique, which has become the essential methodology for tackling large data critical problems. This includes refined/inverse Strichartz estimates, the existence and almost periodicity of minimal blow up solutions, and the development of long-time Strichartz inequalities. The third part describes wave and Schrödinger maps. Starting by building heuristics about multilinear estimates, it provides a detailed outline of this very active area of geometric/dispersive PDE. It focuses on concepts and ideas and should provide graduate students with a stepping stone to this exciting direction of research.
Global Solutions Of Nonlinear Schrodinger Equations
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Author : Jean Bourgain
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Global Solutions Of Nonlinear Schrodinger Equations written by Jean Bourgain and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Differential equations, Partial categories.
This volume presents recent progress in the theory of nonlinear dispersive equations, primarily the nonlinear Schrodinger (NLS) equation. The Cauchy problem for defocusing NLS with critical nonlinearity is discussed. New techniques and results are described on global existence and properties of solutions with Large Cauchy data. Current research in harmonic analysis around Strichartz's inequalities and its relevance to nonlinear PDE is presented and several topics in NLS theory on bounded domains are reviewed. Using the NLS as an example, the book offers comprehensive insight on current research related to dispersive equations and Hamiltonian PDEs.
The Discrete Nonlinear Schr Dinger Equation
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Author : Panayotis G. Kevrekidis
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-07-07
The Discrete Nonlinear Schr Dinger Equation written by Panayotis G. Kevrekidis and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-07 with Science categories.
This book constitutes the first effort to summarize a large volume of results obtained over the past 20 years in the context of the Discrete Nonlinear Schrödinger equation and the physical settings that it describes.
The Nonlinear Schr Dinger Equation
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Author : Gadi Fibich
language : en
Publisher: Springer
Release Date : 2015-03-06
The Nonlinear Schr Dinger Equation written by Gadi Fibich and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-06 with Mathematics categories.
This book is an interdisciplinary introduction to optical collapse of laser beams, which is modelled by singular (blow-up) solutions of the nonlinear Schrödinger equation. With great care and detail, it develops the subject including the mathematical and physical background and the history of the subject. It combines rigorous analysis, asymptotic analysis, informal arguments, numerical simulations, physical modelling, and physical experiments. It repeatedly emphasizes the relations between these approaches, and the intuition behind the results. The Nonlinear Schrödinger Equation will be useful to graduate students and researchers in applied mathematics who are interested in singular solutions of partial differential equations, nonlinear optics and nonlinear waves, and to graduate students and researchers in physics and engineering who are interested in nonlinear optics and Bose-Einstein condensates. It can be used for courses on partial differential equations, nonlinear waves, and nonlinear optics. Gadi Fibich is a Professor of Applied Mathematics at Tel Aviv University. “This book provides a clear presentation of the nonlinear Schrodinger equation and its applications from various perspectives (rigorous analysis, informal analysis, and physics). It will be extremely useful for students and researchers who enter this field.” Frank Merle, Université de Cergy-Pontoise and Institut des Hautes Études Scientifiques, France
Kam Tori For Perturbations Of The Defocusing Nls Equation
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Author : Massimiliano Berti
language : en
Publisher:
Release Date : 2018
Kam Tori For Perturbations Of The Defocusing Nls Equation written by Massimiliano Berti and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Implicit functions categories.
The Nonlinear Schr Dinger Equation
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Author : Catherine Sulem
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-30
The Nonlinear Schr Dinger Equation written by Catherine Sulem and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-30 with Mathematics categories.
Filling the gap between the mathematical literature and applications to domains, the authors have chosen to address the problem of wave collapse by several methods ranging from rigorous mathematical analysis to formal aymptotic expansions and numerical simulations.