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The Nonlinear Schrodinger Equation
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Book Synopsis The Nonlinear Schrödinger Equation by : Gadi Fibich
Download or read book The Nonlinear Schrödinger Equation written by Gadi Fibich and published by Springer. This book was released on 2015-03-06 with total page 870 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an interdisciplinary introduction to optical collapse of laser beams, which is modelled by singular (blow-up) solutions of the nonlinear Schrödinger equation. With great care and detail, it develops the subject including the mathematical and physical background and the history of the subject. It combines rigorous analysis, asymptotic analysis, informal arguments, numerical simulations, physical modelling, and physical experiments. It repeatedly emphasizes the relations between these approaches, and the intuition behind the results. The Nonlinear Schrödinger Equation will be useful to graduate students and researchers in applied mathematics who are interested in singular solutions of partial differential equations, nonlinear optics and nonlinear waves, and to graduate students and researchers in physics and engineering who are interested in nonlinear optics and Bose-Einstein condensates. It can be used for courses on partial differential equations, nonlinear waves, and nonlinear optics. Gadi Fibich is a Professor of Applied Mathematics at Tel Aviv University. “This book provides a clear presentation of the nonlinear Schrodinger equation and its applications from various perspectives (rigorous analysis, informal analysis, and physics). It will be extremely useful for students and researchers who enter this field.” Frank Merle, Université de Cergy-Pontoise and Institut des Hautes Études Scientifiques, France
Book Synopsis The Nonlinear Schrödinger Equation by : Catherine Sulem
Download or read book The Nonlinear Schrödinger Equation written by Catherine Sulem and published by Springer Science & Business Media. This book was released on 1999-06-18 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: Filling the gap between the mathematical literature and applications to domains, the authors have chosen to address the problem of wave collapse by several methods ranging from rigorous mathematical analysis to formal aymptotic expansions and numerical simulations.
Author :Panayotis G. Kevrekidis Publisher :Springer Science & Business Media ISBN 13 :3540891994 Total Pages :417 pages Book Rating :4.5/5 (48 download)
Book Synopsis The Discrete Nonlinear Schrödinger Equation by : Panayotis G. Kevrekidis
Download or read book The Discrete Nonlinear Schrödinger Equation written by Panayotis G. Kevrekidis and published by Springer Science & Business Media. This book was released on 2009-07-07 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Handbook of Exact Solutions to the Nonlinear Schrödinger Equations (Second Edition) by : USAMA. AL KHAWAJA
Download or read book Handbook of Exact Solutions to the Nonlinear Schrödinger Equations (Second Edition) written by USAMA. AL KHAWAJA and published by Institute of Physics Publishing. This book was released on 2024-06-28 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Book Synopsis Nonlinear Fractional Schrödinger Equations in R^N by : Vincenzo Ambrosio
Download or read book Nonlinear Fractional Schrödinger Equations in R^N written by Vincenzo Ambrosio and published by Springer Nature. This book was released on 2021-04-19 with total page 669 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents recent results concerning nonlinear fractional elliptic problems in the whole space. More precisely, it investigates the existence, multiplicity and qualitative properties of solutions for fractional Schrödinger equations by applying suitable variational and topological methods. The book is mainly intended for researchers in pure and applied mathematics, physics, mechanics, and engineering. However, the material will also be useful for students in higher semesters and young researchers, as well as experienced specialists working in the field of nonlocal PDEs. This is the first book to approach fractional nonlinear Schrödinger equations by applying variational and topological methods.
Book Synopsis Optical Communication Theory and Techniques by : Enrico Forestieri
Download or read book Optical Communication Theory and Techniques written by Enrico Forestieri and published by Springer Science & Business Media. This book was released on 2006-01-26 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the advent of optical communications, a greattechnological effort has been devoted to the exploitation of the huge bandwidth of optical fibers. Sta- ing from a few Mb/s single channel systems, a fast and constant technological development has led to the actual 10 Gb/s per channel dense wavelength - vision multiplexing (DWDM) systems, with dozens of channels on a single fiber. Transmitters and receivers are now ready for 40 Gb/s, whereas hundreds of channels can be simultaneously amplified by optical amplifiers. Nevertheless, despite such a pace in technological progress, optical c- munications are still in a primitive stage if compared, for instance, to radio communications: the widely spread on-off keying (OOK) modulation format is equivalent to the rough amplitude modulation (AM) format, whereas the DWDM technique is nothing more than the optical version of the frequency - vision multiplexing (FDM) technique. Moreover, adaptive equalization, ch- nel coding or maximum likelihood detection are still considered something “exotic” in the optical world. This is mainly due to the favourable char- teristics of the fiber optic channel (large bandwidth, low attenuation, channel stability, ...), which so far allowed us to use very simple transmission and detection techniques.
Book Synopsis Nonlinear Fiber Optics by : Govind P. Agrawal
Download or read book Nonlinear Fiber Optics written by Govind P. Agrawal and published by Academic Press. This book was released on 2007 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the 3rd edition appeared, a fast evolution of the field has occurred. The fourth edition of this classic work provides an up-to-date account of the nonlinear phenomena occurring inside optical fibers. The contents include such important topics as self- and cross-phase modulation, stimulated Raman and Brillouin scattering, four-wave mixing, modulation instability, and optical solitons. Many new figures have been added to help illustrate the concepts discussed in the book. New to this edition are chapters on highly nonlinear fibers and and the novel nonlinear effects that have been observed in these fibers since 2000. Such a chapter should be of interest to people in the field of new wavelengths generation, which has potential application in medical diagnosis and treatments, spectroscopy, new wavelength lasers and light sources, etc. Continues to be industry bestseller providing unique source of comprehensive coverage on the subject of nonlinear fiber optics Fourth Edition is a completely up-to-date treatment of the nonlinear phenomena occurring inside optical fibers Includes 2 NEW CHAPTERS on the properties of highly nonlinear fibers and their novel nonlinear effects
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.
Book Synopsis Defocusing Nonlinear Schrödinger Equations by : Benjamin Dodson
Download or read book Defocusing Nonlinear Schrödinger Equations written by Benjamin Dodson and published by Cambridge University Press. This book was released on 2019-03-28 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Introduction to Nonlinear Dispersive Equations by : Felipe Linares
Download or read book Introduction to Nonlinear Dispersive Equations written by Felipe Linares and published by Springer. This book was released on 2014-12-15 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
Book Synopsis Solitons and the Inverse Scattering Transform by : Mark J. Ablowitz
Download or read book Solitons and the Inverse Scattering Transform written by Mark J. Ablowitz and published by SIAM. This book was released on 2006-05-15 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: A study, by two of the major contributors to the theory, of the inverse scattering transform and its application to problems of nonlinear dispersive waves that arise in fluid dynamics, plasma physics, nonlinear optics, particle physics, crystal lattice theory, nonlinear circuit theory and other areas. A soliton is a localised pulse-like nonlinear wave that possesses remarkable stability properties. Typically, problems that admit soliton solutions are in the form of evolution equations that describe how some variable or set of variables evolve in time from a given state. The equations may take a variety of forms, for example, PDEs, differential difference equations, partial difference equations, and integrodifferential equations, as well as coupled ODEs of finite order. What is surprising is that, although these problems are nonlinear, the general solution that evolves from almost arbitrary initial data may be obtained without approximation.
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.
Book Synopsis Localization And Energy Transfer In Nonlinear Systems, Proceedings Of The Third Conference by : Luis Vazquez
Download or read book Localization And Energy Transfer In Nonlinear Systems, Proceedings Of The Third Conference written by Luis Vazquez and published by World Scientific. This book was released on 2003-05-22 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This conference was the third meeting organized in the framework of the European LOCNET project. The main topics discussed by this international research collaboration were localization by nonlinearity and spatial discreteness, and energy transfer (in crystals, biomolecules and Josephson arrays).
Download or read book Chiral Solitons written by Keh-fei Liu and published by World Scientific. This book was released on 1987-04-01 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: This review volume on topological and nontopological chiral solitons presents a global view on the current developments of this field in particle and nuclear physics. The book addresses problems in quantization, restoration of translational and rotational symmetry, and the field theoretical approach to solitons which are common problems in the field of solitons. Primarily aimed for graduate students and the novice in the field, the collected articless cover a broad spectrum of topics in formalism as well as phenomenology.
Book Synopsis Nonlinear Dirac Equation: Spectral Stability of Solitary Waves by : Nabile Boussaïd
Download or read book Nonlinear Dirac Equation: Spectral Stability of Solitary Waves written by Nabile Boussaïd and published by American Mathematical Soc.. This book was released on 2019-11-21 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
