Semi Classical Analysis For Nonlinear Schrdinger Equations

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

Author : Remi Carles
Publisher : World Scientific
ISBN 13 : 9811227926
Total Pages : 367 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Semi-classical Analysis For Nonlinear Schrodinger Equations: Wkb Analysis, Focal Points, Coherent States (Second Edition) by : Remi Carles

Download or read book Semi-classical Analysis For Nonlinear Schrodinger Equations: Wkb Analysis, Focal Points, Coherent States (Second Edition) written by Remi Carles and published by World Scientific. This book was released on 2020-10-05 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Semi-Classical Analysis for Nonlinear Schr??dinger Equations

Author :
Publisher :
ISBN 13 : 9814471747
Total Pages : pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Semi-Classical Analysis for Nonlinear Schr??dinger Equations by :

Download or read book Semi-Classical Analysis for Nonlinear Schr??dinger Equations written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Semi-classical Analysis for Nonlinear Schrödinger Equations

Author : Rémi Carles
Publisher : World Scientific Publishing Company Incorporated
ISBN 13 : 9812793127
Total Pages : 243 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Semi-classical Analysis for Nonlinear Schrödinger Equations by : Rémi Carles

Download or read book Semi-classical Analysis for Nonlinear Schrödinger Equations written by Rémi Carles and published by World Scientific Publishing Company Incorporated. This book was released on 2008 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Semi-classical Analysis for Nonlinear Schrödinger Equations

Author : Rémi Carles
Publisher : World Scientific Publishing Company
ISBN 13 : 9789811227905
Total Pages : 0 pages
Book Rating : 4.2/5 (279 download)

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Book Synopsis Semi-classical Analysis for Nonlinear Schrödinger Equations by : Rémi Carles

Download or read book Semi-classical Analysis for Nonlinear Schrödinger Equations written by Rémi Carles and published by World Scientific Publishing Company. This book was released on 2020-09-29 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Schrdinger 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.

Semiclassical Soliton Ensembles for the Focusing Nonlinear Schrodinger Equation (AM-154)

Author : Spyridon Kamvissis
Publisher : Princeton University Press
ISBN 13 : 069111482X
Total Pages : 281 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Semiclassical Soliton Ensembles for the Focusing Nonlinear Schrodinger Equation (AM-154) by : Spyridon Kamvissis

Download or read book Semiclassical Soliton Ensembles for the Focusing Nonlinear Schrodinger Equation (AM-154) written by Spyridon Kamvissis and published by Princeton University Press. This book was released on 2003-09-07 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing an asymptotic analysis via completely integrable techniques, of the initial value problem for the focusing nonlinear Schrodinger equation in the semiclassical asymptotic regime, this text exploits complete integrability to establish pointwise asymptotics for this problem's solution.

Semiclassical Analysis for Diffusions and Stochastic Processes

Author : Vassili N. Kolokoltsov
Publisher : Springer
ISBN 13 : 3540465871
Total Pages : 360 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Semiclassical Analysis for Diffusions and Stochastic Processes by : Vassili N. Kolokoltsov

Download or read book Semiclassical Analysis for Diffusions and Stochastic Processes written by Vassili N. Kolokoltsov and published by Springer. This book was released on 2007-12-03 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: The monograph is devoted mainly to the analytical study of the differential, pseudo-differential and stochastic evolution equations describing the transition probabilities of various Markov processes. These include (i) diffusions (in particular,degenerate diffusions), (ii) more general jump-diffusions, especially stable jump-diffusions driven by stable Lévy processes, (iii) complex stochastic Schrödinger equations which correspond to models of quantum open systems. The main results of the book concern the existence, two-sided estimates, path integral representation, and small time and semiclassical asymptotics for the Green functions (or fundamental solutions) of these equations, which represent the transition probability densities of the corresponding random process. The boundary value problem for Hamiltonian systems and some spectral asymptotics ar also discussed. Readers should have an elementary knowledge of probability, complex and functional analysis, and calculus.

Wigner Measure and Semiclassical Limits of Nonlinear Schrödinger Equations

Author : Ping Zhang
Publisher : American Mathematical Soc.
ISBN 13 : 9780821847015
Total Pages : 197 pages
Book Rating : 4.8/5 (47 download)

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Book Synopsis Wigner Measure and Semiclassical Limits of Nonlinear Schrödinger Equations by : Ping Zhang

Download or read book Wigner Measure and Semiclassical Limits of Nonlinear Schrödinger Equations written by Ping Zhang and published by American Mathematical Soc.. This book was released on 2008 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Semiclassical Soliton Ensembles for the Focusing Nonlinear Schrödinger Equation

Author : Spyridon Kamvissis
Publisher :
ISBN 13 :
Total Pages : 367 pages
Book Rating : 4.:/5 (495 download)

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Book Synopsis Semiclassical Soliton Ensembles for the Focusing Nonlinear Schrödinger Equation by : Spyridon Kamvissis

Download or read book Semiclassical Soliton Ensembles for the Focusing Nonlinear Schrödinger Equation written by Spyridon Kamvissis and published by . This book was released on 2002 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Semilinear Schrodinger Equations

Author : Thierry Cazenave
Publisher : American Mathematical Soc.
ISBN 13 : 0821833995
Total Pages : 346 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Semilinear Schrodinger Equations by : Thierry Cazenave

Download or read book Semilinear Schrodinger Equations written by Thierry Cazenave and published by American Mathematical Soc.. This book was released on 2003 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: The nonlinear Schrodinger equation has received a great deal of attention from mathematicians, particularly because of its applications to nonlinear optics. This book presents various mathematical aspects of the nonlinear Schrodinger equation. It studies both problems of local nature and problems of global nature.

Wigner Measure and Semiclassical Limits of Nonlinear Schrödinger Equations

Author : Ping Zhang
Publisher : American Mathematical Soc.
ISBN 13 : 9780821883563
Total Pages : 212 pages
Book Rating : 4.8/5 (835 download)

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Book Synopsis Wigner Measure and Semiclassical Limits of Nonlinear Schrödinger Equations by : Ping Zhang

Download or read book Wigner Measure and Semiclassical Limits of Nonlinear Schrödinger Equations written by Ping Zhang and published by American Mathematical Soc.. This book was released on with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.

Semiclassical Analysis

Author : Maciej Zworski
Publisher : American Mathematical Soc.
ISBN 13 : 0821883208
Total Pages : 448 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Semiclassical Analysis by : Maciej Zworski

Download or read book Semiclassical Analysis written by Maciej Zworski and published by American Mathematical Soc.. This book was released on 2012 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: "...A graduate level text introducing readers to semiclassical and microlocal methods in PDE." -- from xi.

Semiclassical Analysis

Author : Maciej Zworski
Publisher : American Mathematical Society
ISBN 13 : 1470470624
Total Pages : 431 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Semiclassical Analysis by : Maciej Zworski

Download or read book Semiclassical Analysis written by Maciej Zworski and published by American Mathematical Society. This book was released on 2022-05-09 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an excellent, comprehensive introduction to semiclassical analysis. I believe it will become a standard reference for the subject. —Alejandro Uribe, University of Michigan Semiclassical analysis provides PDE techniques based on the classical-quantum (particle-wave) correspondence. These techniques include such well-known tools as geometric optics and the Wentzel–Kramers–Brillouin approximation. Examples of problems studied in this subject are high energy eigenvalue asymptotics and effective dynamics for solutions of evolution equations. From the mathematical point of view, semiclassical analysis is a branch of microlocal analysis which, broadly speaking, applies harmonic analysis and symplectic geometry to the study of linear and nonlinear PDE. The book is intended to be a graduate level text introducing readers to semiclassical and microlocal methods in PDE. It is augmented in later chapters with many specialized advanced topics which provide a link to current research literature.

Nonlinear Dispersive Partial Differential Equations and Inverse Scattering

Author : Peter D. Miller
Publisher : Springer Nature
ISBN 13 : 1493998064
Total Pages : 528 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Nonlinear Dispersive Partial Differential Equations and Inverse Scattering by : Peter D. Miller

Download or read book Nonlinear Dispersive Partial Differential Equations and Inverse Scattering written by Peter D. Miller and published by Springer Nature. This book was released on 2019-11-14 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Differential Equations, Asymptotic Analysis, and Mathematical Physics

Author : Michael Demuth
Publisher : John Wiley & Sons
ISBN 13 : 9783055017698
Total Pages : 436 pages
Book Rating : 4.0/5 (176 download)

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Book Synopsis Differential Equations, Asymptotic Analysis, and Mathematical Physics by : Michael Demuth

Download or read book Differential Equations, Asymptotic Analysis, and Mathematical Physics written by Michael Demuth and published by John Wiley & Sons. This book was released on 1997 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of original papers, associated with the International Conference on Partial Differential Equations, held in Potsdam, July 29 to August 2, 1996. The conference has taken place every year on a high scientific level since 1991; this event is connected with the activities of the Max Planck Research Group for Partial Differential Equations at Potsdam. Outstanding researchers and specialists from Armenia, Belarus, Belgium, Bulgaria, Canada, China, France, Germany, Great Britain, India, Israel, Italy, Japan, Poland, Romania, Russia, Spain, Sweden, Switzerland, Ukraine, and the USA contribute to this volume. The main topics concern recent progress in partial differential equations, microlocal analysis, pseudo-differential operators on manifolds with singularities, aspects in differential geometry and index theory, operator theory and operator algebras, stochastic spectral analysis, semigroups, Dirichlet forms, Schrodinger operators, semiclassical analysis, and scattering theory.

Semiclassical Soliton Ensembles for the Focusing Nonlinear Schrödinger Equation (AM-154)

Author : Spyridon Kamvissis
Publisher : Princeton University Press
ISBN 13 : 1400837189
Total Pages : 280 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Semiclassical Soliton Ensembles for the Focusing Nonlinear Schrödinger Equation (AM-154) by : Spyridon Kamvissis

Download or read book Semiclassical Soliton Ensembles for the Focusing Nonlinear Schrödinger Equation (AM-154) written by Spyridon Kamvissis and published by Princeton University Press. This book was released on 2003-08-18 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book represents the first asymptotic analysis, via completely integrable techniques, of the initial value problem for the focusing nonlinear Schrödinger equation in the semiclassical asymptotic regime. This problem is a key model in nonlinear optical physics and has increasingly important applications in the telecommunications industry. The authors exploit complete integrability to establish pointwise asymptotics for this problem's solution in the semiclassical regime and explicit integration for the underlying nonlinear, elliptic, partial differential equations suspected of governing the semiclassical behavior. In doing so they also aim to explain the observed gradient catastrophe for the underlying nonlinear elliptic partial differential equations, and to set forth a detailed, pointwise asymptotic description of the violent oscillations that emerge following the gradient catastrophe. To achieve this, the authors have extended the reach of two powerful analytical techniques that have arisen through the asymptotic analysis of integrable systems: the Lax-Levermore-Venakides variational approach to singular limits in integrable systems, and Deift and Zhou's nonlinear Steepest-Descent/Stationary Phase method for the analysis of Riemann-Hilbert problems. In particular, they introduce a systematic procedure for handling certain Riemann-Hilbert problems with poles accumulating on curves in the plane. This book, which includes an appendix on the use of the Fredholm theory for Riemann-Hilbert problems in the Hölder class, is intended for researchers and graduate students of applied mathematics and analysis, especially those with an interest in integrable systems, nonlinear waves, or complex analysis.

Discrete and Continuous Nonlinear Schrödinger Systems

Author : M. J. Ablowitz
Publisher : Cambridge University Press
ISBN 13 : 9780521534376
Total Pages : 276 pages
Book Rating : 4.5/5 (343 download)

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Book Synopsis Discrete and Continuous Nonlinear Schrödinger Systems by : M. J. Ablowitz

Download or read book Discrete and Continuous Nonlinear Schrödinger Systems written by M. J. Ablowitz and published by Cambridge University Press. This book was released on 2004 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a detailed mathematical analysis of scattering theory, obtains soliton solutions, and analyzes soliton interactions, both scalar and vector.

Analysis and Topology in Nonlinear Differential Equations

Author : Djairo G de Figueiredo
Publisher : Springer
ISBN 13 : 3319042149
Total Pages : 465 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Analysis and Topology in Nonlinear Differential Equations by : Djairo G de Figueiredo

Download or read book Analysis and Topology in Nonlinear Differential Equations written by Djairo G de Figueiredo and published by Springer. This book was released on 2014-06-16 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of articles presented at the Workshop for Nonlinear Analysis held in João Pessoa, Brazil, in September 2012. The influence of Bernhard Ruf, to whom this volume is dedicated on the occasion of his 60th birthday, is perceptible throughout the collection by the choice of themes and techniques. The many contributors consider modern topics in the calculus of variations, topological methods and regularity analysis, together with novel applications of partial differential equations. In keeping with the tradition of the workshop, emphasis is given to elliptic operators inserted in different contexts, both theoretical and applied. Topics include semi-linear and fully nonlinear equations and systems with different nonlinearities, at sub- and supercritical exponents, with spectral interactions of Ambrosetti-Prodi type. Also treated are analytic aspects as well as applications such as diffusion problems in mathematical genetics and finance and evolution equations related to electromechanical devices.