Author: USAMA. AL KHAWAJAPublisher: Institute of Physics Publishing
ISBN: 9780750359559
Category : Science
Languages : en
Pages : 0
Book Description
Handbook of Exact Solutions to the Nonlinear Schrödinger Equations (Second Edition)
Author: USAMA. AL KHAWAJAPublisher: Institute of Physics Publishing
ISBN: 9780750359559
Category : Science
Languages : en
Pages : 0
Book Description
The Discrete Nonlinear Schrödinger Equation
Author: Panayotis G. KevrekidisPublisher: Springer Science & Business Media
ISBN: 3540891994
Category : Science
Languages : en
Pages : 417
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.
Discrete and Continuous Nonlinear Schrödinger Systems
Author: M. J. AblowitzPublisher: Cambridge University Press
ISBN: 9780521534376
Category : Mathematics
Languages : en
Pages : 276
Book Description
This book presents a detailed mathematical analysis of scattering theory, obtains soliton solutions, and analyzes soliton interactions, both scalar and vector.
Solutions of Nonlinear Schrӧdinger Systems
Author: Zhijie ChenPublisher: Springer
ISBN: 3662454785
Category : Mathematics
Languages : en
Pages : 191
Book Description
The existence and qualitative properties of nontrivial solutions for some important nonlinear Schrӧdinger systems have been studied in this thesis. For a well-known system arising from nonlinear optics and Bose-Einstein condensates (BEC), in the subcritical case, qualitative properties of ground state solutions, including an optimal parameter range for the existence, the uniqueness and asymptotic behaviors, have been investigated and the results could firstly partially answer open questions raised by Ambrosetti, Colorado and Sirakov. In the critical case, a systematical research on ground state solutions, including the existence, the nonexistence, the uniqueness and the phase separation phenomena of the limit profile has been presented, which seems to be the first contribution for BEC in the critical case. Furthermore, some quite different phenomena were also studied in a more general critical system. For the classical Brezis-Nirenberg critical exponent problem, the sharp energy estimate of least energy solutions in a ball has been investigated in this study. Finally, for Ambrosetti type linearly coupled Schrӧdinger equations with critical exponent, an optimal result on the existence and nonexistence of ground state solutions for different coupling constants was also obtained in this thesis. These results have many applications in Physics and PDEs.
Schrödinger Equations in Nonlinear Systems
Author: Wu-Ming LiuPublisher: Springer
ISBN: 9811365814
Category : Science
Languages : en
Pages : 576
Book Description
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.
Solitons and the Inverse Scattering Transform
Author: Mark J. AblowitzPublisher: SIAM
ISBN: 089871477X
Category : Mathematics
Languages : en
Pages : 433
Book Description
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.
The Nonlinear Schrödinger Equation
Author: Catherine SulemPublisher: Springer Science & Business Media
ISBN: 0387227687
Category : Mathematics
Languages : en
Pages : 363
Book Description
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.
Minimax Theorems
Author: Michel WillemPublisher: Springer Science & Business Media
ISBN: 1461241464
Category : Mathematics
Languages : en
Pages : 168
Book Description
Many boundary value problems are equivalent to Au=O (1) where A : X --+ Y is a mapping between two Banach spaces. When the problem is variational, there exists a differentiable functional rand inf.
Optical Communication Theory and Techniques
Author: Enrico ForestieriPublisher: Springer Science & Business Media
ISBN: 0387231366
Category : Computers
Languages : en
Pages : 214
Book Description
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.
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