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Schrödinger Equations in Nonlinear Systems

✍ Scribed by Wu-Ming Liu, Emmanuel Kengne

Publisher
Springer Singapore
Year
2019
Tongue
English
Leaves
576
Edition
1st ed.
Category
Library
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✦ Synopsis

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.


✦ Table of Contents

Front Matter ....Pages i-xvi
Overview of Nonlinear Schrödinger Equations (Wu-Ming Liu, Emmanuel Kengne)....Pages 1-13
Well-Posedness of Nonlocal Boundary-Value Problems and Schrödinger Equations (Wu-Ming Liu, Emmanuel Kengne)....Pages 15-43
Nonlinear Schrödinger Equations of Single Transmission Lines (Wu-Ming Liu, Emmanuel Kengne)....Pages 45-105
Derivative Nonlinear Schrödinger Equations for Single Transmission Lines (Wu-Ming Liu, Emmanuel Kengne)....Pages 107-155
NLS Equations for the System of the Nonlinear Transmission Lines Coupled by Capacitor (C_{2}) (Wu-Ming Liu, Emmanuel Kengne)....Pages 157-191
Inhomogeneous Nonlinear Schrödinger Equations of Bose–Einstein Condensates with Two-Body Interactions (Wu-Ming Liu, Emmanuel Kengne)....Pages 193-263
Dynamics of BECs with Two- and Three-Body Interactions (Wu-Ming Liu, Emmanuel Kengne)....Pages 265-318
Multicomponent NLS Type Equations and BECs (Wu-Ming Liu, Emmanuel Kengne)....Pages 319-391
Two-Component Nonlinear Schrödinger Equations for Spin-1 BECs (Wu-Ming Liu, Emmanuel Kengne)....Pages 393-436
Multicomponent Nonlinear Schrödinger Equations for Spin-1 and Spin-2 BECs (Wu-Ming Liu, Emmanuel Kengne)....Pages 437-511
Higher Dimensional Nonlinear Schrödinger Equations of Bose–Einstein Condensates (Wu-Ming Liu, Emmanuel Kengne)....Pages 513-563
Back Matter ....Pages 565-569

✦ Subjects

Physics; Mathematical Methods in Physics; Mathematical Physics; Condensed Matter Physics; Applications of Nonlinear Dynamics and Chaos Theory

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