Nonlinear Dispersive Equations
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Nonlinear Dispersive Equations
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Author : Terence Tao
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Nonlinear Dispersive Equations written by Terence Tao 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 2006 with Mathematics categories.
"Starting only with a basic knowledge of graduate real analysis and Fourier analysis, the text first presents basic nonlinear tools such as the bootstrap method and perturbation theory in the simpler context of nonlinear ODE, then introduces the harmonic analysis and geometric tools used to control linear dispersive PDE. These methods are then combined to study four model nonlinear dispersive equations. Through extensive exercises, diagrams, and informal discussion, the book gives a rigorous theoretical treatment of the material, the real-world intuition and heuristics that underlie the subject, as well as mentioning connections with other areas of PDE, harmonic analysis, and dynamical systems.".
Introduction To Nonlinear Dispersive Equations
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Author : Felipe Linares
language : en
Publisher: Springer
Release Date : 2014-12-15
Introduction To Nonlinear Dispersive Equations written by Felipe Linares and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-15 with Mathematics categories.
This textbook introduces the well-posedness theory for initial-value problems of nonlinear, dispersive partial differential equations, with special focus on two key models, the Korteweg–de Vries equation and the nonlinear Schrödinger equation. A concise and self-contained treatment of background material (the Fourier transform, interpolation theory, Sobolev spaces, and the linear Schrödinger equation) prepares the reader to understand the main topics covered: the initial-value problem for the nonlinear Schrödinger equation and the generalized Korteweg–de Vries equation, properties of their solutions, and a survey of general classes of nonlinear dispersive equations of physical and mathematical significance. Each chapter ends with an expert account of recent developments and open problems, as well as exercises. The final chapter gives a detailed exposition of local well-posedness for the nonlinear Schrödinger equation, taking the reader to the forefront of recent research. The second edition of Introduction to Nonlinear Dispersive Equations builds upon the success of the first edition by the addition of updated material on the main topics, an expanded bibliography, and new exercises. Assuming only basic knowledge of complex analysis and integration theory, this book will enable graduate students and researchers to enter this actively developing field.
Nonlinear Dispersive Equations
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Author : Terence Tao
language : en
Publisher: American Mathematical Soc.
Release Date :
Nonlinear Dispersive Equations written by Terence Tao 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 with Mathematics categories.
"Starting only with a basic knowledge of graduate real analysis and Fourier analysis, the text first presents basic nonlinear tools such as the bootstrap method and perturbation theory in the simpler context of nonlinear ODE, then introduces the harmonic analysis and geometric tools used to control linear dispersive PDE. These methods are then combined to study four model nonlinear dispersive equations. Through extensive exercises, diagrams, and informal discussion, the book gives a rigorous theoretical treatment of the material, the real-world intuition and heuristics that underlie the subject, as well as mentioning connections with other areas of PDE, harmonic analysis, and dynamical systems.".
Dispersive Equations And Nonlinear Waves
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Author : Herbert Koch
language : en
Publisher: Birkhäuser
Release Date : 2014-07-31
Dispersive Equations And Nonlinear Waves written by Herbert Koch and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-31 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.
Dispersive Partial Differential Equations
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Author : M. Burak Erdoğan
language : en
Publisher: Cambridge University Press
Release Date : 2016-05-12
Dispersive Partial Differential Equations written by M. Burak Erdoğan 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 2016-05-12 with Mathematics categories.
Introduces nonlinear dispersive partial differential equations in a detailed yet elementary way without compromising the depth and richness of the subject.
Nonlinear Dispersive Waves
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Author : Mark J. Ablowitz
language : en
Publisher: Cambridge University Press
Release Date : 2011-09-08
Nonlinear Dispersive Waves written by Mark J. Ablowitz 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 2011-09-08 with Mathematics categories.
The field of nonlinear dispersive waves has developed enormously since the work of Stokes, Boussinesq and Korteweg–de Vries (KdV) in the nineteenth century. In the 1960s, researchers developed effective asymptotic methods for deriving nonlinear wave equations, such as the KdV equation, governing a broad class of physical phenomena that admit special solutions including those commonly known as solitons. This book describes the underlying approximation techniques and methods for finding solutions to these and other equations. The concepts and methods covered include wave dispersion, asymptotic analysis, perturbation theory, the method of multiple scales, deep and shallow water waves, nonlinear optics including fiber optic communications, mode-locked lasers and dispersion-managed wave phenomena. Most chapters feature exercise sets, making the book suitable for advanced courses or for self-directed learning. Graduate students and researchers will find this an excellent entry to a thriving area at the intersection of applied mathematics, engineering and physical science.
Semilinear Schrodinger Equations
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Author : Thierry Cazenave
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Semilinear Schrodinger Equations written by Thierry Cazenave 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 2003 with Mathematics categories.
The nonlinear Schrodinger equation has received a great deal of attention from mathematicians, particularly because of its applications to nonlinear optics. This book presents various mathematical aspects of the nonlinear Schrodinger equation. It studies both problems of local nature and problems of global nature.
Mathematical Aspects Of Nonlinear Dispersive Equations Am 163
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Author : Jean Bourgain
language : en
Publisher: Princeton University Press
Release Date : 2007-04-29
Mathematical Aspects Of Nonlinear Dispersive Equations Am 163 written by Jean Bourgain and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-29 with Mathematics categories.
This collection of new and original papers on mathematical aspects of nonlinear dispersive equations includes both expository and technical papers that reflect a number of recent advances in the field. The expository papers describe the state of the art and research directions. The technical papers concentrate on a specific problem and the related analysis and are addressed to active researchers. The book deals with many topics that have been the focus of intensive research and, in several cases, significant progress in recent years, including hyperbolic conservation laws, Schrödinger operators, nonlinear Schrödinger and wave equations, and the Euler and Navier-Stokes equations.
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