Defocusing Nonlinear Schrödinger Equations
Title | Defocusing Nonlinear Schrödinger Equations PDF eBook |
Author | Benjamin Dodson |
Publisher | Cambridge University Press |
Pages | 256 |
Release | 2019-03-28 |
Genre | Mathematics |
ISBN | 1108681670 |
This study of Schrödinger equations with power-type nonlinearity provides a great deal of insight into other dispersive partial differential equations and geometric partial differential equations. It presents important proofs, using tools from harmonic analysis, microlocal analysis, functional analysis, and topology. This includes a new proof of Keel–Tao endpoint Strichartz estimates, and a new proof of Bourgain's result for radial, energy-critical NLS. It also provides a detailed presentation of scattering results for energy-critical and mass-critical equations. This book is suitable as the basis for a one-semester course, and serves as a useful introduction to nonlinear Schrödinger equations for those with a background in harmonic analysis, functional analysis, and partial differential equations.
Defocusing Nonlinear Schrödinger Equations
Title | Defocusing Nonlinear Schrödinger Equations PDF eBook |
Author | Benjamin Dodson |
Publisher | Cambridge University Press |
Pages | 255 |
Release | 2019-03-28 |
Genre | Mathematics |
ISBN | 1108472087 |
Explores Schrödinger equations with power-type nonlinearity, with scattering results for mass- and energy-critical Schrödinger equations.
The Defocusing Nonlinear Schr?dinger Equation
Title | The Defocusing Nonlinear Schr?dinger Equation PDF eBook |
Author | Panayotis G. Kevrekidis |
Publisher | SIAM |
Pages | 437 |
Release | 2015-08-04 |
Genre | Mathematics |
ISBN | 1611973945 |
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 Schr?dinger-type models that arise therein.?The Defocusing Nonlinear Schr?dinger Equation?is a broad study of nonlinear?excitations in self-defocusing nonlinear media. It summarizes state-of-the-art knowledge on the defocusing nonlinear Schr?dinger-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 Discrete Nonlinear Schrödinger Equation
Title | The Discrete Nonlinear Schrödinger Equation PDF eBook |
Author | Panayotis G. Kevrekidis |
Publisher | Springer Science & Business Media |
Pages | 417 |
Release | 2009-07-07 |
Genre | Science |
ISBN | 3540891994 |
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 Defocusing NLS Equation and Its Normal Form
Title | The Defocusing NLS Equation and Its Normal Form PDF eBook |
Author | |
Publisher | |
Pages | |
Release | 2014 |
Genre | |
ISBN | 9783037196311 |
The Defocusing Nonlinear Schrödinger Equation with Step-like Oscillatory Data
Title | The Defocusing Nonlinear Schrödinger Equation with Step-like Oscillatory Data PDF eBook |
Author | Samuel Fromm |
Publisher | |
Pages | |
Release | 2021 |
Genre | |
ISBN | 9789178738632 |
Nonlinear Dispersive Equations
Title | Nonlinear Dispersive Equations PDF eBook |
Author | Terence Tao |
Publisher | American Mathematical Soc. |
Pages | 394 |
Release | 2006 |
Genre | Mathematics |
ISBN | 0821841432 |
"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.".