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BL
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| Record Number
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891033
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| Main Entry
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Liu, Wu-Ming
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| Title & Author
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Schrödinger equations in nonlinear systems /\ Wu-Ming Liu, Emmanuel Kengne.
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| Publication Statement
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Singapore :: Springer,, 2019.
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| Page. NO
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1 online resource (xvi, 569 pages) :: illustrations (some color)
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| ISBN
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9789811365805
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: 9789811365812
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: 9789811365829
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: 9789811365836
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: 9811365806
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: 9811365814
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: 9811365822
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: 9811365830
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9789811365805
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| Bibliographies/Indexes
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Includes bibliographical references and index.
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| Contents
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Intro; Preface; Acknowledgements; Contents; 1 Overview of Nonlinear Schrödinger Equations; 1.1 One-dimensional Cubic Nonlinear ... ; 1.2 Derivative Nonlinear Schrödinger Equation; 1.3 Inhomogeneous Nonlinear Schrödinger Equations (Gross-Pitaevskii Equations); 1.4 Multicomponent Nonlinear Schrödinger Equation; References; 2 Well-Posedness of Nonlocal Boundary-Value Problems and Schrödinger Equations; 2.1 Boundary-Value Problem from the Viewpoint of the General Theory of Partial Differential Equations; 2.2 Perturbation of a Two-Point Boundary-Value Problem
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2.2.1 Perturbation of Ill-Posed Boundary-Value Problems by an Integral Term in the Boundary Condition2.2.2 Perturbation of Well-Posed Boundary-Value Problems by Integral Terms in the Boundary Condition; 2.3 Well-Posedness of a Two-Point Boundary-Value Problem in a Layer for a System of Evolution Equations; 2.4 Boundary-Value Problem for Factorized Operators with Dirichlet-Type Boundary Conditions; 2.4.1 Formulation of Problem and Notations; 2.4.2 Uniqueness of Solutions to Problem (2.22)-(2.24); 2.4.3 Existence of Solutions of Problem (2.22)-(2.24)
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3.4 Interacting Signal Packets in the Lossless Network of Fig. 3.1 in Absence of Second-Neighbor Interactions3.4.1 Coupled NLS Equations for the Lossless Discrete Nonlinear Electrical Network of Fig. 3.1 for L3=infty; 3.4.2 Modulational Instability; 3.4.3 Analytical Study of Matter-Wave Solitons in the Network; 3.4.4 Bright-Kink and Kink-Bright Solitary Wave Solutions; References; 4 Derivative Nonlinear Schrödinger Equations for Single Transmission Lines; 4.1 Generation of Nonlinear Modulated Waves in the Lossless Network of Fig. 3.1
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| Abstract
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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.
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| Subject
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Gross-Pitaevskii equations.
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Gross-Pitaevskii equations.
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Mathematical Methods in Physics.
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Applications of Nonlinear Dynamics and Chaos Theory.
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Condensed Matter Physics.
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| Subject
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Mathematical Physics.
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| Dewey Classification
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530.12/4
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| LC Classification
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QC174.26.W28
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| Added Entry
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Kengne, Emmanuel
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