Schr Dinger Equations In Nonlinear Systems
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Semi Classical Analysis For Nonlinear Schr Dinger Equations
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Author : Rmi Carles
language : en
Publisher: World Scientific
Release Date : 2008
Semi Classical Analysis For Nonlinear Schr Dinger Equations written by Rmi Carles and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
These lecture notes review recent results on the high-frequency analysis of nonlinear Schrdinger equations in the presence of an external potential. The book consists of two relatively independent parts: WKB analysis, and caustic crossing. In the first part, the basic linear WKB theory is constructed and then extended to the nonlinear framework. The most difficult supercritical case is discussed in detail, together with some of its consequences concerning instability phenomena. Applications of WKB analysis to functional analysis, in particular to the Cauchy problem for nonlinear Schrdinger equations, are also given. In the second part, caustic crossing is described, especially when the caustic is reduced to a point, and the link with nonlinear scattering operators is investigated.These notes are self-contained and combine selected articles written by the author over the past ten years in a coherent manner, with some simplified proofs. Examples and figures are provided to support the intuition, and comparisons with other equations such as the nonlinear wave equation are provided.
The Defocusing Nonlinear Schr Dinger Equation
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Author : Panayotis G. Kevrekidis
language : en
Publisher: SIAM
Release Date : 2015-08-04
The Defocusing Nonlinear Schr Dinger Equation written by Panayotis G. Kevrekidis and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-04 with Mathematics categories.
Bose?Einstein condensation is a phase transition in which a fraction of particles of a boson gas condenses into the same quantum state known as the Bose?Einstein condensate (BEC). The aim of this book is to present a wide array of findings in the realm of BECs and on the nonlinear SchrÓdinger-type models that arise therein.÷The Defocusing Nonlinear SchrÓdinger Equation÷is a broad study of nonlinear÷excitations in self-defocusing nonlinear media. It summarizes state-of-the-art knowledge on the defocusing nonlinear SchrÓdinger-type models in a single volume and contains a wealth of resources, including over 800 references to relevant articles and monographs and a meticulous index for ease of navigation.
Methods Of Hilbert Spaces In The Theory Of Nonlinear Dynamical Systems
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Author : Krzysztof Kowalski
language : en
Publisher: World Scientific
Release Date : 1994
Methods Of Hilbert Spaces In The Theory Of Nonlinear Dynamical Systems written by Krzysztof Kowalski and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
This book is the first monograph on a new powerful method discovered by the author for the study of nonlinear dynamical systems relying on reduction of nonlinear differential equations to the linear abstract Schrdinger-like equation in Hilbert space. Besides the possibility of unification of many apparently completely different techniques, the ?quantal? Hilbert space formalism introduced enables new original methods to be discovered for solving nonlinear problems arising in investigation of ordinary and partial differential equations as well as difference equations. Applications covered in the book include symmetries and first integrals, linearization transformations, Bcklund transformations, stroboscopic maps, functional equations involving the case of Feigenbaum-Cvitanovic renormalization equations and chaos.
Nonlinear Systems Of Partial Differential Equations
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Author :
language : en
Publisher:
Release Date :
Nonlinear Systems Of Partial Differential Equations written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Semi Classical Analysis For Nonlinear Schr Dinger Equations
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Author : Rémi Carles
language : en
Publisher: World Scientific Publishing Company
Release Date : 2020-09-29
Semi Classical Analysis For Nonlinear Schr Dinger Equations written by Rémi Carles and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-29 with Mathematics categories.
The second edition of this book consists of three parts. The first one is dedicated to the WKB methods and the semi-classical limit before the formation of caustics. The second part treats the semi-classical limit in the presence of caustics, in the special geometric case where the caustic is reduced to a point (or to several isolated points). The third part is new in this edition, and addresses the nonlinear propagation of coherent states. The three parts are essentially independent. Compared with the first edition, the first part is enriched by a new section on multiphase expansions in the case of weakly nonlinear geometric optics, and an application related to this study, concerning instability results for nonlinear Schrdinger equations in negative order Sobolev spaces. The third part is an overview of results concerning nonlinear effects in the propagation of coherent states, in the case of a power nonlinearity, and in the richer case of Hartree-like nonlinearities. It includes explicit formulas of an independent interest, such as generalized Mehler's formula, generalized lens transform.
Harmonic Analysis Method For Nonlinear Evolution Equations I
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Author : Baoxiang Wang
language : en
Publisher: World Scientific
Release Date : 2011
Harmonic Analysis Method For Nonlinear Evolution Equations I written by Baoxiang Wang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
This monograph provides a comprehensive overview on a class of nonlinear dispersive equations, such as nonlinear Schr dinger equation, nonlinear Klein Gordon equation, KdV equation as well as the Navier Stokes equations and the Boltzmann equation. The global wellposedness to the Cauchy problem for those equations are systematically studied by using the Harmonic analysis methods. This book is self-contained and may also be used as an advanced textbook by graduate students in analysis and PDE subjects- and even ambitious undergraduate students.
Solutions Of Nonlinear Schr Dinger Systems
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Author : Zhijie Chen
language : en
Publisher:
Release Date : 2014-12-31
Solutions Of Nonlinear Schr Dinger Systems written by Zhijie Chen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-31 with categories.
Nonlinear Equations
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Author : Daniela Lupo
language : en
Publisher: Birkhauser
Release Date : 2003-01-01
Nonlinear Equations written by Daniela Lupo and has been published by Birkhauser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-01 with Differential equations, Nonlinear categories.
Global Solutions Of Nonlinear Schr Dinger Equations
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Author : Jean Bourgain
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Global Solutions Of Nonlinear Schr Dinger Equations written by Jean Bourgain and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Science categories.
Nonlinear Systems
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Author :
language : en
Publisher: BoD – Books on Demand
Release Date : 2018-07-18
Nonlinear Systems written by and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-18 with Mathematics categories.
This book focuses on several key aspects of nonlinear systems including dynamic modeling, state estimation, and stability analysis. It is intended to provide a wide range of readers in applied mathematics and various engineering disciplines an excellent survey of recent studies of nonlinear systems. With its thirteen chapters, the book brings together important contributions from renowned international researchers to provide an excellent survey of recent studies of nonlinear systems. The first section consists of eight chapters that focus on nonlinear dynamic modeling and analysis techniques, while the next section is composed of five chapters that center on state estimation methods and stability analysis for nonlinear systems.