[PDF] A Numerical Study Of Coupled Nonlinear Schrodinger Equations Arising In Hydrodynamics And Optics eBook

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File Size : 48,28 MB
Release : 2003
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(Uncorrected OCR) Abstract of the thesis entitled A NUMERICAL STUDY OF COUPLED NONLINEAR SCHRODINGER EQUATIONS ARISING IN HYDRODYNAMICS AND OPTICS submitted by Suk-Chong TSANG for the degree of Master of Philosophy at the University of Hong Kong in June 2003 This thesis reports the fmdings of numerical studies of coupled nonlinear Schrodinger equations (CNLS) in both hydrodynamics and optics applications, and its focus was a model for interaction between wavepackets in the framework of CNLS. Generally, group velocity dispersion, self-phase modulation and cross-phase modulation terms are present in these equations. However, intermodal dispersion and linear coupling terms may also exist when CNLS are applied in optics. The interplay between these effects plays a crucial role in pulse evolution. A numerical method, the Hopscotch method, was introduced to solve CNLS. This is a particularly simple method for solving CNLS, and its accuracy was verified by ascertaining the evolution of a single soliton solution of CNLS and comparing this numerical solution with the exact solution. Two applications of CNLS were studied, m hydrodynamics and optics respectively. In hydrodynamics, CNLS is used to govern the interaction of wavepackets in layered fluid. The long-time evolution of periodic solution of CNLS 1 was studied. The initial phase difference, amplitude ratio between perturbations and the ratio between the self-phase and cross-phase modulations were found to be important factors in long-time evolution. Different patterns of evolution may result from different combinations of these three effects mentioned above. In optics, CNLS can be used as the governing equation for wavepackets in directional couplers. Soliton interaction in directional couplers was studied, as their performance can be quite different from how they behave in single-mode fibers. Their behaviour was influenced by group-velocity dispersion, intermodal dispersion and linear coupling terms within the equation.

Author : A. A. Coley
Publisher : American Mathematical Soc.
Page : 460 pages
File Size : 43,23 MB
Release : 2001-01-01
Category : Mathematics
ISBN : 9780821870259

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This book is devoted to a classical topic that has undergone rapid and fruitful development over the past 25 years, namely Backlund and Darboux transformations and their applications in the theory of integrable systems, also known as soliton theory. The book consists of two parts. The first is a series of introductory pedagogical lectures presented by leading experts in the field. They are devoted respectively to Backlund transformations of Painleve equations, to the dressing methodand Backlund and Darboux transformations, and to the classical geometry of Backlund transformations and their applications to soliton theory. The second part contains original contributions that represent new developments in the theory and applications of these transformations. Both the introductorylectures and the original talks were presented at an International Workshop that took place in Halifax, Nova Scotia (Canada). This volume covers virtually all recent developments in the theory and applications of Backlund and Darboux transformations.

Author : Vasile Marinca
Publisher : Springer
Page : 476 pages
File Size : 43,12 MB
Release : 2015-04-02
Category : Technology & Engineering
ISBN : 3319153749

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This book emphasizes in detail the applicability of the Optimal Homotopy Asymptotic Method to various engineering problems. It is a continuation of the book “Nonlinear Dynamical Systems in Engineering: Some Approximate Approaches”, published at Springer in 2011 and it contains a great amount of practical models from various fields of engineering such as classical and fluid mechanics, thermodynamics, nonlinear oscillations, electrical machines and so on. The main structure of the book consists of 5 chapters. The first chapter is introductory while the second chapter is devoted to a short history of the development of homotopy methods, including the basic ideas of the Optimal Homotopy Asymptotic Method. The last three chapters, from Chapter 3 to Chapter 5, are introducing three distinct alternatives of the Optimal Homotopy Asymptotic Method with illustrative applications to nonlinear dynamical systems. The third chapter deals with the first alternative of our approach with two iterations. Five applications are presented from fluid mechanics and nonlinear oscillations. The Chapter 4 presents the Optimal Homotopy Asymptotic Method with a single iteration and solving the linear equation on the first approximation. Here are treated 32 models from different fields of engineering such as fluid mechanics, thermodynamics, nonlinear damped and undamped oscillations, electrical machines and even from physics and biology. The last chapter is devoted to the Optimal Homotopy Asymptotic Method with a single iteration but without solving the equation in the first approximation.

Author : Wu-Ming Liu
Publisher : Springer
Page : 569 pages
File Size : 17,54 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.

Author : Catherine Sulem
Publisher : Springer Science & Business Media
Page : 363 pages
File Size : 41,2 MB
Release : 2007-06-30
Category : Mathematics
ISBN : 0387227687

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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 : Yuri S. Kivshar
Publisher : Academic Press
Page : 557 pages
File Size : 30,25 MB
Release : 2003-06-12
Category : Technology & Engineering
ISBN : 0080538096

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The current research into solitons and their use in fiber optic communications is very important to the future of communications. Since the advent of computer networking and high speed data transmission technology people have been striving to develop faster and more reliable communications media. Optical pulses tend to broaden over relatively short distances due to dispersion, but solitons on the other hand are not as susceptible to the effects of dispersion, and although they are subject to losses due to attenuation they can be amplified without being received and re-transmitted. This book is the first to provide a thorough overview of optical solitons. The main purpose of this book is to present the rapidly developing field of Spatial Optical Solitons starting from the basic concepts of light self-focusing and self-trapping. It will introduce the fundamental concepts of the theory of nonlinear waves and solitons in non-integrated but physically realistic models of nonlinear optics including their stability and dynamics. Also, it will summarize a number of important experimental verification of the basic theoretical predictions and concepts covering the observation of self-focusing in the earlier days of nonlinear optics and the most recent experimental results on spatial solitons, vortex solitons, and soliton interaction & spiraling. * Introduces the fundamental concepts of the theory of nonlinear waves and solitons through realistic models * Material is based on authors' years of experience actively working in and researching the field * Summarizes the most important experimental verification of the basic theories, predictions and concepts of this ever evolving field from the earliest studies to the most recent