Wigner Measure and Semiclassical Limits of Nonlinear Schrödinger Equations

Wigner Measure and Semiclassical Limits of Nonlinear Schrödinger Equations PDF

Author: Ping Zhang

Publisher: American Mathematical Soc.

Published: 2008

Total Pages: 197

ISBN-13: 9780821847015

DOWNLOAD EBOOK →

This book is based on a course entitled ``Wigner measures and semiclassical limits of nonlinear Schrodinger equations,'' which the author taught at the Courant Institute of Mathematical Sciences at New York University in the spring of 2007. The author's main purpose is to apply the theory of semiclassical pseudodifferential operators to the study of various high-frequency limits of equations from quantum mechanics. In particular, the focus of attention is on Wigner measure and recent progress on how to use it as a tool to study various problems arising from semiclassical limits of Schrodinger-type equations. At the end of each chapter, the reader will find references and remarks about recent progress on related problems. The book is self-contained and is suitable for an advanced graduate course on the topic.

Wigner Measure and Semiclassical Limits of Nonlinear Schrödinger Equations

Wigner Measure and Semiclassical Limits of Nonlinear Schrödinger Equations PDF

Author: Ping Zhang

Publisher: American Mathematical Soc.

Published:

Total Pages: 212

ISBN-13: 9780821883563

DOWNLOAD EBOOK →

"This book is based on a course entitled "Wigner measures and semiclassical limits of nonlinear Schrodinger equations," which the author taught at the Courant Institute of Mathematical Sciences at New York University in the spring of 2007. The author's main purpose is to apply the theory of semiclassical pseudodifferential operators to the study of various high-frequency limits of equations from quantum mechanics. In particular, the focus of attention is on Wigner measure and recent progress on how to use it as a tool to study various problems arising from semiclassical limits of Schrodinger-type equations." "At the end of each chapter, the reader will find references and remarks about recent progress on related problems. The book is self-contained and is suitable for an advanced graduate course on the topic."--BOOK JACKET.

Semi-classical Analysis For Nonlinear Schrodinger Equations: Wkb Analysis, Focal Points, Coherent States (Second Edition)

Semi-classical Analysis For Nonlinear Schrodinger Equations: Wkb Analysis, Focal Points, Coherent States (Second Edition) PDF

Author: Remi Carles

Publisher: World Scientific

Published: 2020-10-05

Total Pages: 367

ISBN-13: 9811227926

DOWNLOAD EBOOK →

The second edition of this book consists of three parts. The first one is dedicated to the WKB methods and the semi-classical limit before the formation of caustics. The second part treats the semi-classical limit in the presence of caustics, in the special geometric case where the caustic is reduced to a point (or to several isolated points). The third part is new in this edition, and addresses the nonlinear propagation of coherent states. The three parts are essentially independent.Compared with the first edition, the first part is enriched by a new section on multiphase expansions in the case of weakly nonlinear geometric optics, and an application related to this study, concerning instability results for nonlinear Schrödinger equations in negative order Sobolev spaces.The third part is an overview of results concerning nonlinear effects in the propagation of coherent states, in the case of a power nonlinearity, and in the richer case of Hartree-like nonlinearities. It includes explicit formulas of an independent interest, such as generalized Mehler's formula, generalized lens transform.

Applied Mathematics Entering the 21st Century

Applied Mathematics Entering the 21st Century PDF

Author: James M. Hill

Publisher: SIAM

Published: 2004-04-01

Total Pages: 440

ISBN-13: 9780898715590

DOWNLOAD EBOOK →

Included in this volume are the Invited Talks given at the 5th International Congress of Industrial and Applied Mathematics. The authors of these papers are all acknowledged masters of their fields, having been chosen through a rigorous selection process by a distinguished International Program Committee. This volume presents an overview of contemporary applications of mathematics, with the coverage ranging from the rhythms of the nervous system, to optimal transportation, elasto-plasticity, computational drug design, hydrodynamic and meteorological modeling, and valuation in financial markets. Many papers are direct products of the computer revolution: grid generation, multi-scale modeling, high-dimensional numerical integration, nonlinear optimization, accurate floating-point computations and advanced iterative methods. Other papers demonstrate the close dependence on developments in mathematics itself, and the increasing importance of statistics. Additional topics relate to the study of properties of fluids and fluid-flows, or add to our understanding of Partial Differential Equations.

Recent Progress in Computational and Applied PDES

Recent Progress in Computational and Applied PDES PDF

Author: Tony F. Chan

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 433

ISBN-13: 146150113X

DOWNLOAD EBOOK →

The book discusses some key scientific and technological developments in computational and applied partial differential equations. It covers many areas of scientific computing, including multigrid methods, image processing, finite element analysis and adaptive computations. It also covers software technology, algorithms and applications. Most papers are of research level, and are contributed by some well-known mathematicians and computer scientists. The book will be useful to engineers, computational scientists and graduate students.

Semi-classical Analysis For Nonlinear Schrodinger Equations

Semi-classical Analysis For Nonlinear Schrodinger Equations PDF

Author: Remi Carles

Publisher: World Scientific

Published: 2008-03-04

Total Pages: 256

ISBN-13: 9814471747

DOWNLOAD EBOOK →

These lecture notes review recent results on the high-frequency analysis of nonlinear Schrödinger equations in the presence of an external potential. The book consists of two relatively independent parts: WKB analysis, and caustic crossing. In the first part, the basic linear WKB theory is constructed and then extended to the nonlinear framework. The most difficult supercritical case is discussed in detail, together with some of its consequences concerning instability phenomena. Applications of WKB analysis to functional analysis, in particular to the Cauchy problem for nonlinear Schrödinger equations, are also given. In the second part, caustic crossing is described, especially when the caustic is reduced to a point, and the link with nonlinear scattering operators is investigated.These notes are self-contained and combine selected articles written by the author over the past ten years in a coherent manner, with some simplified proofs. Examples and figures are provided to support the intuition, and comparisons with other equations such as the nonlinear wave equation are provided.

PDF

Author:

Publisher: World Scientific

Published:

Total Pages: 1131

ISBN-13:

DOWNLOAD EBOOK →

Elliptic Partial Differential Equations

Elliptic Partial Differential Equations PDF

Author: Qing Han

Publisher: American Mathematical Soc.

Published: 2011

Total Pages: 161

ISBN-13: 0821853139

DOWNLOAD EBOOK →

This volume is based on PDE courses given by the authors at the Courant Institute and at the University of Notre Dame, Indiana. Presented are basic methods for obtaining various a priori estimates for second-order equations of elliptic type with particular emphasis on maximal principles, Harnack inequalities, and their applications. The equations considered in the book are linear; however, the presented methods also apply to nonlinear problems.

Lanterna Rally - Theme by Grace Themes