Author: Andreas BolleyerPublisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Spectrally Localized Strichartz Estimates and Nonlinear Schrödinger Equations
Strichartz Estimates for Schrödinger Equations with Variable Coefficients
Author: Luc RobbianoPublisher:
ISBN:
Category : Schrödinger equation
Languages : en
Pages : 222
Book Description
The authors prove the (local in time) Stricharz estimates (for the full range of parameters given by the scaling unless the end point) for asymptotically flat and non trapping perturbations of the flat Laplacian in $\mathbb {R} ^n$, $n\geq 2$. The main point of the proof, namely the dispersion estimate, is obtained in constructing a parametrix. The main tool for this construction is the use of the Fourier-Bros-Iagolnitzer (FBI) transform.
Local Smoothing Estimates for Schrödinger Equations on Hyperbolic Space
Author: Andrew LawriePublisher: American Mathematical Society
ISBN: 147046697X
Category : Mathematics
Languages : en
Pages : 178
Book Description
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Korteweg-de Vries and Nonlinear Schrödinger Equations: Qualitative Theory
Author: Peter E. ZhidkovPublisher: Springer
ISBN: 3540452761
Category : Mathematics
Languages : en
Pages : 153
Book Description
- of nonlinear the of solitons the the last 30 theory partial theory During years - has into solutions of a kind a differential special equations (PDEs) possessing grown and in view the attention of both mathematicians field that attracts physicists large and of the of the problems of its novelty problems. Physical important applications for in the under consideration are mo- to the observed, example, equations leading mathematical discoveries is the Makhankov One of the related V.G. by [60]. graph from this field methods that of certain nonlinear by equations possibility studying inverse these to the problem; equations were analyze quantum scattering developed this method of the inverse called solvable the scattering problem (on subject, are by known nonlinear At the the class of for same time, currently example [89,94]). see, the other there is solvable this method is narrow on hand, PDEs sufficiently and, by of differential The latter called the another qualitative theory equations. approach, the of various in includes on pr- investigations well-posedness approach particular solutions such or lems for these the behavior of as stability blowing-up, equations, these and this of approach dynamical systems generated by equations, etc., properties in wider class of a makes it to an problems (maybe possible investigate essentially more general study).
Spectral and Scattering Theory for Second Order Partial Differential Operators
Author: Kiyoshi MochizukiPublisher: CRC Press
ISBN: 1351648942
Category : Mathematics
Languages : en
Pages : 131
Book Description
The book is intended for students of graduate and postgraduate level, researchers in mathematical sciences as well as those who want to apply the spectral theory of second order differential operators in exterior domains to their own field. In the first half of this book, the classical results of spectral and scattering theory: the selfadjointness, essential spectrum, absolute continuity of the continuous spectrum, spectral representations, short-range and long-range scattering are summarized. In the second half, recent results: scattering of Schrodinger operators on a star graph, uniform resolvent estimates, smoothing properties and Strichartz estimates, and some applications are discussed.
Nonlinear Dirac Equation: Spectral Stability of Solitary Waves
Author: Nabile BoussaïdPublisher: American Mathematical Soc.
ISBN: 1470443953
Category : Education
Languages : en
Pages : 297
Book Description
This monograph gives a comprehensive treatment of spectral (linear) stability of weakly relativistic solitary waves in the nonlinear Dirac equation. It turns out that the instability is not an intrinsic property of the Dirac equation that is only resolved in the framework of the second quantization with the Dirac sea hypothesis. Whereas general results about the Dirac-Maxwell and similar equations are not yet available, we can consider the Dirac equation with scalar self-interaction, the model first introduced in 1938. In this book we show that in particular cases solitary waves in this model may be spectrally stable (no linear instability). This result is the first step towards proving asymptotic stability of solitary waves. The book presents the necessary overview of the functional analysis, spectral theory, and the existence and linear stability of solitary waves of the nonlinear Schrödinger equation. It also presents the necessary tools such as the limiting absorption principle and the Carleman estimates in the form applicable to the Dirac operator, and proves the general form of the Dirac-Pauli theorem. All of these results are used to prove the spectral stability of weakly relativistic solitary wave solutions of the nonlinear Dirac equation.
Atti Del ... Congresso Internazionale Dei Matematici ...
Author: Spectral Methods Applied to the Nonlinear Schrödinger Equation
Author: Roger Alan McCoyPublisher:
ISBN:
Category : Schrödinger equation
Languages : en
Pages : 290
Book Description
Author: Sahbi Keraani
Author: Per Sjölin