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 Differential equations, Partial 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.".
Mathematical Aspects Of Nonlinear Dispersive Equations Am 163
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Author : Jean Bourgain
language : en
Publisher: Princeton University Press
Release Date : 2009-01-10
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 2009-01-10 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.
Introduction To Nonlinear Dispersive Equations
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Author : Felipe Linares
language : en
Publisher:
Release Date : 2015-01-31
Introduction To Nonlinear Dispersive Equations written by Felipe Linares and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-31 with categories.
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 : Jaime Angulo Pava
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
Nonlinear Dispersive Equations written by Jaime Angulo Pava 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 2009 with Nonlinear waves categories.
Offers a self-contained presentation of classical 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. This book is suitable for students and mature scientists interested in nonlinear wave phenomena.
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.
Nonlinear Dispersive Equations
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Author : Christian Klein
language : en
Publisher: Springer Nature
Release Date : 2021
Nonlinear Dispersive Equations written by Christian Klein and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Differential equations categories.
Nonlinear Dispersive Equations are partial differential equations that naturally arise in physical settings where dispersion dominates dissipation, notably hydrodynamics, nonlinear optics, plasma physics and Bose-Einstein condensates. The topic has traditionally been approached in different ways, from the perspective of modeling of physical phenomena, to that of the theory of partial differential equations, or as part of the theory of integrable systems. This monograph offers a thorough introduction to the topic, uniting the modeling, PDE and integrable systems approaches for the first time in book form. The presentation focuses on three "universal" families of physically relevant equations endowed with a completely integrable member: the Benjamin-Ono, Davey-Stewartson, and Kadomtsev-Petviashvili equations. These asymptotic models are rigorously derived and qualitative properties such as soliton resolution are studied in detail in both integrable and non-integrable models. Numerical simulations are presented throughout to illustrate interesting phenomena. By presenting and comparing results from different fields, the book aims to stimulate scientific interactions and attract new students and researchers to the topic. To facilitate this, the chapters can be read largely independently of each other and the prerequisites have been limited to introductory courses in PDE theory.
Nonlinear Dispersive Partial Differential Equations And Inverse Scattering
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Author : Peter D. Miller
language : en
Publisher: Springer Nature
Release Date : 2019-11-14
Nonlinear Dispersive Partial Differential Equations And Inverse Scattering written by Peter D. Miller and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-14 with Mathematics categories.
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.
Large Time Behavior Of Solutions Of Linear Dispersive Equations
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Author : Daniel B. Dix
language : en
Publisher: Springer
Release Date : 2006-11-13
Large Time Behavior Of Solutions Of Linear Dispersive Equations written by Daniel B. Dix and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-13 with Mathematics categories.
This book studies the large-time asymptotic behavior of solutions of the pure initial value problem for linear dispersive equations with constant coefficients and homogeneous symbols in one space dimension. Complete matched and uniformly-valid asymptotic expansions are obtained and sharp error estimates are proved. Using the method of steepest descent much new information on the regularity and spatial asymptotics of the solutions are also obtained. Applications to nonlinear dispersive equations are discussed. This monograph is intended for researchers and graduate students of partial differential equations. Familiarity with basic asymptotic, complex and Fourier analysis is assumed.
Annals Of Mathematics Studies
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Author :
language : en
Publisher:
Release Date : 1940
Annals Of Mathematics Studies written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1940 with Differential equations, Nonlinear categories.