Normalized Solutions For Nonlinear Schrodinger Systems
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Existence and Orbital Stability of Normalized Solutions for Nonlinear Schrödinger Equations
| Author | : Tianxiang Gou |
| Publisher | : |
| Total Pages | : 108 |
| Release | : 2017 |
| Genre | : |
| ISBN | : |
In this thesis, we are concerned with the existence and orbital stability of solutions having prescribed -norm for two types of nonlinear Schrödinger equations in , namely a class of coupled nonlinear Schrödinger systems in and a class of fourth-order nonlinear Schrödinger equations in . These two types of nonlinear Schrödinger equations arise in a variety of mathematical and physical models, and have drawn wide attention to research in recent years. From a physical point of view, such solutions are often referred as normalized solutions, which correspond to critical points of the underlying energy functional restricted to -norm constraint. The main ingredients of our proofs are variational methods.
Nonlinear Analysis - Theory and Methods
| Author | : Nikolaos S. Papageorgiou |
| Publisher | : Springer |
| Total Pages | : 577 |
| Release | : 2019-02-26 |
| Genre | : Mathematics |
| ISBN | : 3030034305 |
This book emphasizes those basic abstract methods and theories that are useful in the study of nonlinear boundary value problems. The content is developed over six chapters, providing a thorough introduction to the techniques used in the variational and topological analysis of nonlinear boundary value problems described by stationary differential operators. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear equations as well as their applications to various processes arising in the applied sciences. They show how these diverse topics are connected to other important parts of mathematics, including topology, functional analysis, mathematical physics, and potential theory. Throughout the book a nice balance is maintained between rigorous mathematics and physical applications. The primary readership includes graduate students and researchers in pure and applied nonlinear analysis.
Semilinear Schrodinger Equations
| Author | : Thierry Cazenave |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 346 |
| Release | : 2003 |
| Genre | : Mathematics |
| ISBN | : 0821833995 |
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.
Discrete and Continuous Nonlinear Schrödinger Systems
| Author | : M. J. Ablowitz |
| Publisher | : Cambridge University Press |
| Total Pages | : 276 |
| Release | : 2004 |
| Genre | : Mathematics |
| ISBN | : 9780521534376 |
This book presents a detailed mathematical analysis of scattering theory, obtains soliton solutions, and analyzes soliton interactions, both scalar and vector.
The Nonlinear Schrödinger Equation
| Author | : Gadi Fibich |
| Publisher | : Springer |
| Total Pages | : 870 |
| Release | : 2015-03-06 |
| Genre | : Mathematics |
| ISBN | : 3319127489 |
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
Solitons in Optical Communications
| Author | : Akira Hasegawa |
| Publisher | : |
| Total Pages | : 344 |
| Release | : 1995 |
| Genre | : Science |
| ISBN | : |
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.
Korteweg-de Vries and Nonlinear Schrödinger Equations: Qualitative Theory
| Author | : Peter E. Zhidkov |
| Publisher | : Springer |
| Total Pages | : 153 |
| Release | : 2003-07-01 |
| Genre | : Mathematics |
| ISBN | : 3540452761 |
- 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).
Schrödinger Equations in Nonlinear Systems
| Author | : Wu-Ming Liu |
| Publisher | : Springer |
| Total Pages | : 569 |
| Release | : 2019-03-20 |
| Genre | : Science |
| ISBN | : 9811365814 |
This book explores the diverse types of Schrödinger equations that appear in nonlinear systems in general, with a specific focus on nonlinear transmission networks and Bose–Einstein Condensates. In the context of nonlinear transmission networks, it employs various methods to rigorously model the phenomena of modulated matter-wave propagation in the network, leading to nonlinear Schrödinger (NLS) equations. Modeling these phenomena is largely based on the reductive perturbation method, and the derived NLS equations are then used to methodically investigate the dynamics of matter-wave solitons in the network. In the context of Bose–Einstein condensates (BECs), the book analyzes the dynamical properties of NLS equations with the external potential of different types, which govern the dynamics of modulated matter-waves in BECs with either two-body interactions or both two- and three-body interatomic interactions. It also discusses the method of investigating both the well-posedness and the ill-posedness of the boundary problem for linear and nonlinear Schrödinger equations and presents new results. Using simple examples, it then illustrates the results on the boundary problems. For both nonlinear transmission networks and Bose–Einstein condensates, the results obtained are supplemented by numerical calculations and presented as figures.
