Mathematical Aspects Of Nonlinear Dispersive Equations Am 163 PDF Download
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Author | : Jean Bourgain |
Publisher | : Princeton University Press |
Total Pages | : 309 |
Release | : 2009-01-10 |
Genre | : Mathematics |
ISBN | : 1400827795 |
Download Mathematical Aspects of Nonlinear Dispersive Equations (AM-163) Book in PDF, ePub and Kindle
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.
Author | : |
Publisher | : |
Total Pages | : 300 |
Release | : 1940 |
Genre | : Differential equations, Nonlinear |
ISBN | : 9780691128603 |
Download Annals of Mathematics Studies Book in PDF, ePub and Kindle
Author | : Alessandro Michelangeli |
Publisher | : Springer |
Total Pages | : 292 |
Release | : 2017-08-01 |
Genre | : Mathematics |
ISBN | : 3319589040 |
Download Advances in Quantum Mechanics Book in PDF, ePub and Kindle
This volume collects recent contributions on the contemporary trends in the mathematics of quantum mechanics, and more specifically in mathematical problems arising in quantum many-body dynamics, quantum graph theory, cold atoms, unitary gases, with particular emphasis on the developments of the specific mathematical tools needed, including: linear and non-linear Schrödinger equations, topological invariants, non-commutative geometry, resonances and operator extension theory, among others. Most of contributors are international leading experts or respected young researchers in mathematical physics, PDE, and operator theory. All their material is the fruit of recent studies that have already become a reference in the community. Offering a unified perspective of the mathematics of quantum mechanics, it is a valuable resource for researchers in the field.
Author | : Felipe Linares |
Publisher | : Springer Science & Business Media |
Total Pages | : 263 |
Release | : 2009-02-21 |
Genre | : Mathematics |
ISBN | : 0387848991 |
Download Introduction to Nonlinear Dispersive Equations Book in PDF, ePub and Kindle
The aim of this textbook is to introduce the theory of nonlinear dispersive equations to graduate students in a constructive way. The first three chapters are dedicated to preliminary material, such as Fourier transform, interpolation theory and Sobolev spaces. The authors then proceed to use the linear Schrodinger equation to describe properties enjoyed by general dispersive equations. This information is then used to treat local and global well-posedness for the semi-linear Schrodinger equations. The end of each chapter contains recent developments and open problems, as well as exercises.
Author | : Jaime Angulo Pava |
Publisher | : American Mathematical Soc. |
Total Pages | : 272 |
Release | : 2009 |
Genre | : Mathematics |
ISBN | : 0821848976 |
Download Nonlinear Dispersive Equations Book in PDF, ePub and Kindle
This book provides a self-contained presentation of classical and new methods for studying wave phenomena that are related to the existence and stability of solitary and periodic travelling wave solutions for nonlinear dispersive evolution equations. Simplicity, concrete examples, and applications are emphasized throughout in order to make the material easily accessible. The list of classical nonlinear dispersive equations studied include Korteweg-de Vries, Benjamin-Ono, and Schrodinger equations. Many special Jacobian elliptic functions play a role in these examples. The author brings the reader to the forefront of knowledge about some aspects of the theory and motivates future developments in this fascinating and rapidly growing field. The book can be used as an instructive study guide as well as a reference by students and mature scientists interested in nonlinear wave phenomena.
Author | : Marko Kostić |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 734 |
Release | : 2021-11-22 |
Genre | : Mathematics |
ISBN | : 3110763524 |
Download Selected Topics in Almost Periodicity Book in PDF, ePub and Kindle
Covers uniformly recurrent solutions and c-almost periodic solutions of abstract Volterra integro-differential equations as well as various generalizations of almost periodic functions in Lebesgue spaces with variable coefficients. Treats multi-dimensional almost periodic type functions and their generalizations in adequate detail.
Author | : Terence Tao |
Publisher | : American Mathematical Soc. |
Total Pages | : 394 |
Release | : 2006 |
Genre | : Differential equations, Partial |
ISBN | : 0821841432 |
Download Nonlinear Dispersive Equations Book in PDF, ePub and Kindle
"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.".
Author | : Herbert Koch |
Publisher | : Birkhäuser |
Total Pages | : 0 |
Release | : 2014-07-31 |
Genre | : Mathematics |
ISBN | : 9783034807357 |
Download Dispersive Equations and Nonlinear Waves Book in PDF, ePub and Kindle
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.
Author | : Peter D. Miller |
Publisher | : Springer Nature |
Total Pages | : 528 |
Release | : 2019-11-14 |
Genre | : Mathematics |
ISBN | : 1493998064 |
Download Nonlinear Dispersive Partial Differential Equations and Inverse Scattering Book in PDF, ePub and Kindle
This volume contains lectures and invited papers from the Focus Program on "Nonlinear Dispersive Partial Differential Equations and Inverse Scattering" held at the Fields Institute from July 31-August 18, 2017. The conference brought together researchers in completely integrable systems and PDE with the goal of advancing the understanding of qualitative and long-time behavior in dispersive nonlinear equations. The program included Percy Deift’s Coxeter lectures, which appear in this volume together with tutorial lectures given during the first week of the focus program. The research papers collected here include new results on the focusing nonlinear Schrödinger (NLS) equation, the massive Thirring model, and the Benjamin-Bona-Mahoney equation as dispersive PDE in one space dimension, as well as the Kadomtsev-Petviashvili II equation, the Zakharov-Kuznetsov equation, and the Gross-Pitaevskii equation as dispersive PDE in two space dimensions. The Focus Program coincided with the fiftieth anniversary of the discovery by Gardner, Greene, Kruskal and Miura that the Korteweg-de Vries (KdV) equation could be integrated by exploiting a remarkable connection between KdV and the spectral theory of Schrodinger's equation in one space dimension. This led to the discovery of a number of completely integrable models of dispersive wave propagation, including the cubic NLS equation, and the derivative NLS equation in one space dimension and the Davey-Stewartson, Kadomtsev-Petviashvili and Novikov-Veselov equations in two space dimensions. These models have been extensively studied and, in some cases, the inverse scattering theory has been put on rigorous footing. It has been used as a powerful analytical tool to study global well-posedness and elucidate asymptotic behavior of the solutions, including dispersion, soliton resolution, and semiclassical limits.
Author | : Jean Bourgain |
Publisher | : American Mathematical Soc. |
Total Pages | : 193 |
Release | : 1999 |
Genre | : Differential equations, Partial |
ISBN | : 0821819194 |
Download Global Solutions of Nonlinear Schrodinger Equations Book in PDF, ePub and Kindle
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.