Exact Solutions for a Generalized Nonlinear Schrödinger Equation PDF Download

Author: Morris, J. Ll. (John Ll.)
Publisher: University of Waterloo, Faculty of Mathematics
ISBN:
Category : Differential equations, Nonlinear
Languages : en
Pages : 22

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Book Description
Abstract: "Exact solutions of a generalized nonlinear Schrödinger equation [formula] are obtained by transforming the equation to one whose coefficients satisfy a simple algebraic relationship. The transformed equation also yields conservation laws and sufficient conditions for boundedness and blow-up of solutions for the original equation."

Author: Usama Al Khawaja
Publisher: Institute of Physics Publishing
ISBN: 9780750324298
Category : Science
Languages : en
Pages : 396

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Book Description
This book collects all known solutions to the nonlinear Schrödinger equation (NLSE) in one resource. In addition, the book organizes the solutions by classifying and grouping them based on aspects and symmetries they possess. Although most of the solutions presented in this book have been derived elsewhere using various methods, the authors present a systematic derivation of many solutions and even include new derivations. They have also presented symmetries and reductions that connect different solutions through transformations and enable classifying new solutions into known classes. For the user to verify that the presented solutions do satisfy the NLSE, this monumental work is accompanied by Mathematica Notebooks containing all solutions. This work also features a large number of figures, and animations are included to help visualize solutions and their dynamics.

Author: University of Waterloo. Department of Computer Science
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Book Description

Author: Yong Liu
Publisher: Springer Nature
ISBN: 3030324567
Category : Technology & Engineering
Languages : en
Pages : 1004

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Book Description
This book discusses the recent advances in natural computation, fuzzy systems and knowledge discovery. Presenting selected, peer-reviewed papers from the 15th International Conference on Natural Computation, Fuzzy Systems and Knowledge Discovery (ICNC-FSKD 2019), held in Kunming, China, from 20 to 22 July 2019, it is a useful resource for researchers, including professors and graduate students, as well as R&D staff in industry.

Author: Gadi Fibich
Publisher: Springer
ISBN: 3319127489
Category : Mathematics
Languages : en
Pages : 870

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Book Description
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

Author: Shi-Hai Dong
Publisher: Springer Science & Business Media
ISBN: 9400719175
Category : Science
Languages : en
Pages : 299

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Book Description
Higher dimensional theories have attracted much attention because they make it possible to reduce much of physics in a concise, elegant fashion that unifies the two great theories of the 20th century: Quantum Theory and Relativity. This book provides an elementary description of quantum wave equations in higher dimensions at an advanced level so as to put all current mathematical and physical concepts and techniques at the reader’s disposal. A comprehensive description of quantum wave equations in higher dimensions and their broad range of applications in quantum mechanics is provided, which complements the traditional coverage found in the existing quantum mechanics textbooks and gives scientists a fresh outlook on quantum systems in all branches of physics. In Parts I and II the basic properties of the SO(n) group are reviewed and basic theories and techniques related to wave equations in higher dimensions are introduced. Parts III and IV cover important quantum systems in the framework of non-relativistic and relativistic quantum mechanics in terms of the theories presented in Part II. In particular, the Levinson theorem and the generalized hypervirial theorem in higher dimensions, the Schrödinger equation with position-dependent mass and the Kaluza-Klein theory in higher dimensions are investigated. In this context, the dependence of the energy levels on the dimension is shown. Finally, Part V contains conclusions, outlooks and an extensive bibliography.

Author: Usama Al Khawaja
Publisher:
ISBN: 9780750324274
Category : SCIENCE
Languages : en
Pages :

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Book Description
This book collects all known solutions to the nonlinear Schrödinger equation (NLSE) in one resource. In addition, the book organizes the solutions by classifying and grouping them based on aspects and symmetries they possess. Although most of the solutions presented in this book have been derived elsewhere using various methods, the authors present a systematic derivation of many solutions and even include new derivations. They have also presented symmetries and reductions that connect different solutions through transformations and enable classifying new solutions into known classes. For the user to verify that the presented solutions do satisfy the NLSE, this monumental work is accompanied by Mathematica Notebooks containing all solutions. This work also features a large number of figures, and animations are included to help visualize solutions and their dynamics.

Author: USAMA. AL SAKKAF AL KHAWAJA (LAILA.)
Publisher:
ISBN: 9780750359528
Category :
Languages : en
Pages : 0

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Book Description

Author: Panayotis G. Kevrekidis
Publisher: Springer Science & Business Media
ISBN: 3540891994
Category : Science
Languages : en
Pages : 417

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Book Description
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.

Author: Akira Hasegawa
Publisher:
ISBN:
Category : Science
Languages : en
Pages : 344

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Book Description
Solitons--waves that do not disperse as they travel through a medium--are the most recent and perhaps the most remarkable development in the revolution in telecommunications technology. When coupled with low loss fibers, semiconductor lasers, and erbium doped fibre amplifiers, solitons can carry--with perfect accuracy and at enormous rates--staggering amounts of information across vast distances. Authored by two leaders in the field, this book offers the best, most comprehensive introduction to soliton behavior in optical fibers available. Topics range from the dielectric fiber to the concept of guiding center (average) solitons to transmission control to modulational instability. Solitons in Optical Communications will be avidly read by students and researchers in optical communications and applied mathematics looking for the definitive survey of the hottest topic in telecommunications engineering.