Schrodinger Equations In Nonlinear Systems

Author : Wu-Ming Liu
Publisher : Springer
ISBN 13 : 9811365814
Total Pages : 569 pages
Book Rating : 4.12/5 ( download)

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Download or read book Schrödinger Equations in Nonlinear Systems written by Wu-Ming Liu and published by Springer. This book was released on 2019-03-20 with total page 569 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
ISBN 13 : 0387227687
Total Pages : 363 pages
Book Rating : 4.89/5 ( download)

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Download or read book The Nonlinear Schrödinger Equation written by Catherine Sulem and published by Springer Science & Business Media. This book was released on 2007-06-30 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Usama Al Khawaja
Publisher : Institute of Physics Publishing
ISBN 13 : 9780750324298
Total Pages : 396 pages
Book Rating : 4.95/5 ( download)

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Download or read book Handbook of Exact Solutions to the Nonlinear Schrödinger Equations written by Usama Al Khawaja and published by Institute of Physics Publishing. This book was released on 2019-11-15 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects all known solutions to the nonlinear Schrödinger equation (NLSE) in one resource. In addition, the book organizes the solutions by classifying and grouping them based on aspects and symmetries they possess. Although most of the solutions presented in this book have been derived elsewhere using various methods, the authors present a systematic derivation of many solutions and even include new derivations. They have also presented symmetries and reductions that connect different solutions through transformations and enable classifying new solutions into known classes. For the user to verify that the presented solutions do satisfy the NLSE, this monumental work is accompanied by Mathematica Notebooks containing all solutions. This work also features a large number of figures, and animations are included to help visualize solutions and their dynamics.

Author : Vincenzo Ambrosio
Publisher : Springer Nature
ISBN 13 : 3030602206
Total Pages : 669 pages
Book Rating : 4.08/5 ( download)

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Download or read book Nonlinear Fractional Schrödinger Equations in R^N written by Vincenzo Ambrosio and published by Springer Nature. This book was released on 2021-04-19 with total page 669 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents recent results concerning nonlinear fractional elliptic problems in the whole space. More precisely, it investigates the existence, multiplicity and qualitative properties of solutions for fractional Schrödinger equations by applying suitable variational and topological methods. The book is mainly intended for researchers in pure and applied mathematics, physics, mechanics, and engineering. However, the material will also be useful for students in higher semesters and young researchers, as well as experienced specialists working in the field of nonlocal PDEs. This is the first book to approach fractional nonlinear Schrödinger equations by applying variational and topological methods.

Author : Panayotis G. Kevrekidis
Publisher : Springer Science & Business Media
ISBN 13 : 3540891994
Total Pages : 417 pages
Book Rating : 4.94/5 ( download)

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Download or read book The Discrete Nonlinear Schrödinger Equation written by Panayotis G. Kevrekidis and published by Springer Science & Business Media. This book was released on 2009-07-07 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : M. J. Ablowitz
Publisher : Cambridge University Press
ISBN 13 : 9780521534376
Total Pages : 276 pages
Book Rating : 4.72/5 ( download)

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Download or read book Discrete and Continuous Nonlinear Schrödinger Systems written by M. J. Ablowitz and published by Cambridge University Press. This book was released on 2004 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a detailed mathematical analysis of scattering theory, obtains soliton solutions, and analyzes soliton interactions, both scalar and vector.

Author : Jean Bourgain
Publisher : American Mathematical Soc.
ISBN 13 : 0821819194
Total Pages : 193 pages
Book Rating : 4.97/5 ( download)

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Download or read book Global Solutions of Nonlinear Schrodinger Equations written by Jean Bourgain and published by American Mathematical Soc.. This book was released on 1999 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents recent progress in the theory of nonlinear dispersive equations, primarily the nonlinear Schrodinger (NLS) equation. The Cauchy problem for defocusing NLS with critical nonlinearity is discussed. New techniques and results are described on global existence and properties of solutions with Large Cauchy data. Current research in harmonic analysis around Strichartz's inequalities and its relevance to nonlinear PDE is presented and several topics in NLS theory on bounded domains are reviewed. Using the NLS as an example, the book offers comprehensive insight on current research related to dispersive equations and Hamiltonian PDEs.

Author : Michail D. Todorov
Publisher :
ISBN 13 : 9787560395234
Total Pages : pages
Book Rating : 4.36/5 ( download)

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Download or read book Nonlinear Waves written by Michail D. Todorov and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Benjamin Dodson
Publisher : Cambridge University Press
ISBN 13 : 1108681670
Total Pages : 256 pages
Book Rating : 4.74/5 ( download)

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Download or read book Defocusing Nonlinear Schrödinger Equations written by Benjamin Dodson and published by Cambridge University Press. This book was released on 2019-03-28 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study of Schrödinger equations with power-type nonlinearity provides a great deal of insight into other dispersive partial differential equations and geometric partial differential equations. It presents important proofs, using tools from harmonic analysis, microlocal analysis, functional analysis, and topology. This includes a new proof of Keel–Tao endpoint Strichartz estimates, and a new proof of Bourgain's result for radial, energy-critical NLS. It also provides a detailed presentation of scattering results for energy-critical and mass-critical equations. This book is suitable as the basis for a one-semester course, and serves as a useful introduction to nonlinear Schrödinger equations for those with a background in harmonic analysis, functional analysis, and partial differential equations.

Author : Xiao-feng Pang
Publisher : World Scientific
ISBN 13 : 9814481238
Total Pages : 644 pages
Book Rating : 4.36/5 ( download)

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Download or read book Quantum Mechanics In Nonlinear Systems written by Xiao-feng Pang and published by World Scientific. This book was released on 2005-04-18 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the history of physics and science, quantum mechanics has served as the foundation of modern science. This book discusses the properties of microscopic particles in nonlinear systems, principles of the nonlinear quantum mechanical theory, and its applications in condensed matter, polymers and biological systems.The book is essentially composed of three parts. The first part presents a review of linear quantum mechanics, as well as theoretical and experimental fundamentals that establish the nonlinear quantum mechanical theory. The theory itself and its essential features are covered in the second part. In the final part, extensive applications of this theory in physics, biology and polymer are introduced. The whole volume forms a complete system of nonlinear quantum mechanics.The book is intended for researchers, graduate students as well as upper-level undergraduates.