[PDF] The Nonequilibrium Discrete Nonlinear Schrodinger Equation eBook

Author : Panayotis G. Kevrekidis
Publisher : Springer Science & Business Media
Page : 417 pages
File Size : 48,57 MB
Release : 2009-07-07
Category : Science
ISBN : 3540891994

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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 : Guoping Zhang
Publisher :
Page : 0 pages
File Size : 12,62 MB
Release : 2024-07-30
Category :
ISBN : 9789811290275

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The book is devoted to rigorous mathematical results on discrete nonlinear Schrödinger equations (DNLS), including the initial value problem of the time-dependent DNLS and the standing wave of the stationary DNLS.The stationary DNLS equations appear as equations for the profile of the standing wave in evolutionary DNLS. The book mainly presents well-localized, finite-energy solutions that represent solitary standing waves (breathers in the terminology of nonlinear science), while some other types of solutions are considered as well. The approach accepted in this book is variational, based on various critical point theorems of the mountain pass and linking type, as well as constrained minimization.The book covers the existence of solutions and their properties under various physically reasonable assumptions on linear and nonlinear potentials. It also contains a number of open problems which might be possible thesis topics for fresh PhD students. The results presented are scattered over a large number of research articles and have never been presented in a monograph form. In addition, there are necessary material from the spectral theory of discrete Schrödinger operators, time-dependent DNLS, and a brief presentation of critical point theorems used in the book.

Author : M. J. Ablowitz
Publisher : Cambridge University Press
Page : 276 pages
File Size : 20,99 MB
Release : 2004
Category : Mathematics
ISBN : 9780521534376

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This book presents a detailed mathematical analysis of scattering theory, obtains soliton solutions, and analyzes soliton interactions, both scalar and vector.

Author : Andrea Puglisi
Publisher : MDPI
Page : 335 pages
File Size : 38,2 MB
Release : 2018-09-04
Category : Mathematics
ISBN : 3038970573

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This book is a printed edition of the Special Issue "Thermodynamics and Statistical Mechanics of Small Systems" that was published in Entropy

Author : Luis Vazquez
Publisher : World Scientific
Page : 382 pages
File Size : 15,86 MB
Release : 1996-06-20
Category :
ISBN : 981454809X

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This is the first of two Euroconferences aimed at addressing the issues of Nonlinearity and Disorder. The 1995 Euroconference was devoted to the mathematical, numerical and experimental studies related to the Klein-Gordon and Schrödinger systems. The Euroconference was organized around main lectures in each area to introduce the main concepts and stimulate discussions. The mathematical studies covered the functional anlaysis and stochastic techniques applied to the general Klein-Gordon and Schrödinger wave equations. Also a panoramic view of the numerical schemes was presented to simulate the above equations, as well as an overview of the applications of such systems in the areas of condensed matter, optical physics, new materials and biophysics. Special attention was devoted to the discrete Schrödinger and Klein-Gordon systems and their applications.

Author : Wu-Ming Liu
Publisher : Springer
Page : 569 pages
File Size : 24,14 MB
Release : 2019-03-20
Category : Science
ISBN : 9811365814

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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.