On Multi Component Nonlinear Schr Dinger Equation With Pt Symmetry
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On Multi Component Nonlinear Schr Dinger Equation With Pt Symmetry
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Author : Junaid Idrees Mustafa
language : en
Publisher:
Release Date : 2019
On Multi Component Nonlinear Schr Dinger Equation With Pt Symmetry written by Junaid Idrees Mustafa and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.
On The Discrete Nonlinear Schr Dinger Equation With Pt Symmetry
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Author : Amal Jasim Mohammed
language : en
Publisher:
Release Date : 2018
On The Discrete Nonlinear Schr Dinger Equation With Pt Symmetry written by Amal Jasim Mohammed and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.
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 Discrete Nonlinear Schr Dinger Equation
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Author : Panayotis G. Kevrekidis
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-07-07
The Discrete Nonlinear Schr Dinger Equation written by Panayotis G. Kevrekidis and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-07 with Science categories.
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.
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.
Schrodinger Equations
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Author : Jessica Renee Taylor
language : en
Publisher:
Release Date : 2019
Schrodinger Equations written by Jessica Renee Taylor and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.
This dissertation is composed of work on two types of Schrodinger equations: the nonlinear Schrodinger equation with dipolar interactions (dipolar NLS) and the parity-time (PT) symmetric linear Schrodinger equation. In the dipolar NLS work, we use a gradient-descent method to compute 3D ground states of the equation. We discover that highly-prolate traps, whose long axis is parallel to the dipoles, can give rise to "candlestick" ground states. Direct numerical simulations of the dipolar NLS equation reveal that the nucleus of the candlestick mode undergoes collapse, while obtaining a highly flat, pancake shape. The rate of this anisotropic collapse scales differently from what occurs in isotropic collapse. Stability analysis reveals a surprising cusp point in the mass vs. chemical potential curve, which may serve as a signature for these dynamics. In addition, PT linear Schrodinger equations with complex PT-symmetric periodic potentials are studied analytically and computationally. The possible symmetries of the band-dispersion functions and associated Floquet-Bloch states are identified. Using singular perturbation analysis, we show that band-dispersion functions become complex-valued following the closure of a spectral gap at a degenerate point. Furthermore, we analyze the effect of highly-localized perturbations using asymptotic techniques. These analytical results are elucidated by detailed computations. These results shed new light on the irreversible nature of the phase transition that takes place as the band-dispersion functions become complex
Nonlinear Reaction Diffusion Convection Equations
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Author : Roman Cherniha
language : en
Publisher: CRC Press
Release Date : 2017-11-02
Nonlinear Reaction Diffusion Convection Equations written by Roman Cherniha and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-02 with Mathematics categories.
It is well known that symmetry-based methods are very powerful tools for investigating nonlinear partial differential equations (PDEs), notably for their reduction to those of lower dimensionality (e.g. to ODEs) and constructing exact solutions. This book is devoted to (1) search Lie and conditional (non-classical) symmetries of nonlinear RDC equations, (2) constructing exact solutions using the symmetries obtained, and (3) their applications for solving some biologically and physically motivated problems. The book summarises the results derived by the authors during the last 10 years and those obtained by some other authors.
Nonlinear Schrodinger Equation
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Author : Catherine Sulem
language : en
Publisher:
Release Date : 1999-05-01
Nonlinear Schrodinger Equation written by Catherine Sulem and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-05-01 with categories.
Symmetries Of The Nonlinear Schr Dinger Equation
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Author : B. Grébert
language : en
Publisher:
Release Date : 1999
Symmetries Of The Nonlinear Schr Dinger Equation written by B. Grébert and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with categories.
Invariant Measures For Stochastic Nonlinear Schr Dinger Equations
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Author : Jialin Hong
language : en
Publisher:
Release Date : 2019
Invariant Measures For Stochastic Nonlinear Schr Dinger Equations written by Jialin Hong and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Stochastic differential equations categories.
This book provides some recent advance in the study of stochastic nonlinear Schrödinger equations and their numerical approximations, including the well-posedness, ergodicity, symplecticity and multi-symplecticity. It gives an accessible overview of the existence and uniqueness of invariant measures for stochastic differential equations, introduces geometric structures including symplecticity and (conformal) multi-symplecticity for nonlinear Schrödinger equations and their numerical approximations, and studies the properties and convergence errors of numerical methods for stochastic nonlinear Schrödinger equations. This book will appeal to researchers who are interested in numerical analysis, stochastic analysis, ergodic theory, partial differential equation theory, etc.