Semi Classical Analysis For Nonlinear Schr Dinger Equations
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Semi Classical Analysis For Nonlinear Schrodinger Equations Wkb Analysis Focal Points Coherent States Second Edition
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Author : Remi Carles
language : en
Publisher: World Scientific
Release Date : 2020-10-05
Semi Classical Analysis For Nonlinear Schrodinger Equations Wkb Analysis Focal Points Coherent States Second Edition written by Remi 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 2020-10-05 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 Schrödinger 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.
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.
Geometric Analysis And Pdes
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Author : Matthew J. Gursky
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-06-26
Geometric Analysis And Pdes written by Matthew J. Gursky 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 2009-06-26 with Mathematics categories.
This volume contains lecture notes on key topics in geometric analysis, a growing mathematical subject which uses analytical techniques, mostly of partial differential equations, to treat problems in differential geometry and mathematical physics.
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 Schr?dinger-type models that arise therein. The Defocusing Nonlinear Schr?dinger Equation is a broad study of nonlinear excitations in self-defocusing nonlinear media. It summarizes state-of-the-art knowledge on the defocusing nonlinear Schr?dinger-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.
Communications On Applied Nonlinear Analysis
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Author :
language : en
Publisher:
Release Date : 2006
Communications On Applied Nonlinear Analysis written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Nonlinear functional analysis categories.
Control Theory And Inverse Problems
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Author : Kaïs Ammari
language : en
Publisher: Springer Nature
Release Date : 2024-11-07
Control Theory And Inverse Problems written by Kaïs Ammari and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-07 with Science categories.
This volume presents a timely overview of control theory and inverse problems, and highlights recent advances in these active research areas. The chapters are based on talks given at the spring school "Control Theory & Inverse Problems” held in Monastir, Tunisia in May 2023. In addition to providing a snapshot of these two areas, chapters also highlight breakthroughs on more specific topics, such as: Control of hyperbolic systems The Helffer-Nier Conjecture Rapid stabilization of the discretized Vlasov system Exponential stability of a delayed thermoelastic system Control Theory and Inverse Problems will be a valuable resource for both established researchers as well as more junior members of the community.
Lectures On Non Linear Wave Equations
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Author : Christopher Donald Sogge
language : en
Publisher:
Release Date : 2008
Lectures On Non Linear Wave Equations written by Christopher Donald Sogge and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
Presents an account of the basic facts concerning the linear wave equation and the methods from harmonic analysis that are necessary when studying nonlinear hyperbolic differential equations. This book examines quasilinear equations with small data where the Klainerman-Sobolev inequalities and weighted space-time estimates are introduced.
Current Trends In Mathematical Analysis And Its Interdisciplinary Applications
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Author : Hemen Dutta
language : en
Publisher: Springer Nature
Release Date : 2019-08-23
Current Trends In Mathematical Analysis And Its Interdisciplinary Applications written by Hemen Dutta and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-23 with Mathematics categories.
This book explores several important aspects of recent developments in the interdisciplinary applications of mathematical analysis (MA), and highlights how MA is now being employed in many areas of scientific research. Each of the 23 carefully reviewed chapters was written by experienced expert(s) in respective field, and will enrich readers’ understanding of the respective research problems, providing them with sufficient background to understand the theories, methods and applications discussed. The book’s main goal is to highlight the latest trends and advances, equipping interested readers to pursue further research of their own. Given its scope, the book will especially benefit graduate and PhD students, researchers in the applied sciences, educators, and engineers with an interest in recent developments in the interdisciplinary applications of mathematical analysis.
Discrete And Continuous Dynamical Systems
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Author :
language : en
Publisher:
Release Date : 2003
Discrete And Continuous Dynamical Systems written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Differentiable dynamical systems categories.
Solitons
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Author : Mohamed Atef Helal
language : en
Publisher: Springer Nature
Release Date : 2022-11-12
Solitons written by Mohamed Atef Helal and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-12 with Science categories.
This newly updated volume of the Encyclopedia of Complexity and Systems Science (ECSS) presents several mathematical models that describe this physical phenomenon, including the famous non-linear equation Korteweg-de-Vries (KdV) that represents the canonical form of solitons. Also, there exists a class of nonlinear partial differential equations that led to solitons, e.g., Kadomtsev-Petviashvili (KP), Klein-Gordon (KG), Sine-Gordon (SG), Non-Linear Schrödinger (NLS), Korteweg-de-Vries Burger’s (KdVB), etc. Different linear mathematical methods can be used to solve these models analytically, such as the Inverse Scattering Transformation (IST), Adomian Decomposition Method, Variational Iteration Method (VIM), Homotopy Analysis Method (HAM) and Homotopy Perturbation Method (HPM). Other non-analytic methods use the computational techniques available in such popular mathematical packages as Mathematica, Maple, and MATLAB. The main purpose of this volume is to provide physicists, engineers, and their students with the proper methods and tools to solve the soliton equations, and to discover the new possibilities of using solitons in multi-disciplinary areas ranging from telecommunications to biology, cosmology, and oceanographic studies.