Dispersive Nonlinear Problems In Mathematical Physics
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Dispersive Nonlinear Problems In Mathematical Physics
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Author : Piero D'Ancona
language : en
Publisher:
Release Date : 2005
Dispersive Nonlinear Problems In Mathematical Physics written by Piero D'Ancona and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Science categories.
Nonlinear Dispersive Equations
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Author : Christian Klein
language : en
Publisher: Springer Nature
Release Date : 2022-02-23
Nonlinear Dispersive Equations written by Christian Klein and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-23 with Mathematics categories.
Nonlinear Dispersive Equations are partial differential equations that naturally arise in physical settings where dispersion dominates dissipation, notably hydrodynamics, nonlinear optics, plasma physics and Bose–Einstein condensates. The topic has traditionally been approached in different ways, from the perspective of modeling of physical phenomena, to that of the theory of partial differential equations, or as part of the theory of integrable systems. This monograph offers a thorough introduction to the topic, uniting the modeling, PDE and integrable systems approaches for the first time in book form. The presentation focuses on three "universal" families of physically relevant equations endowed with a completely integrable member: the Benjamin–Ono, Davey–Stewartson, and Kadomtsev–Petviashvili equations. These asymptotic models are rigorously derived and qualitative properties such as soliton resolution are studied in detail in both integrable and non-integrable models. Numerical simulations are presented throughout to illustrate interesting phenomena. By presenting and comparing results from different fields, the book aims to stimulate scientific interactions and attract new students and researchers to the topic. To facilitate this, the chapters can be read largely independently of each other and the prerequisites have been limited to introductory courses in PDE theory.
Dispersive Partial Differential Equations
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Author : M. Burak Erdoğan
language : en
Publisher: Cambridge University Press
Release Date : 2016-05-12
Dispersive Partial Differential Equations written by M. Burak Erdoğan and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-12 with Mathematics categories.
Introduces nonlinear dispersive partial differential equations in a detailed yet elementary way without compromising the depth and richness of the subject.
Nonlinear Dispersive Waves
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Author : Mark J. Ablowitz
language : en
Publisher: Cambridge University Press
Release Date : 2011-09-08
Nonlinear Dispersive Waves written by Mark J. Ablowitz and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-08 with Mathematics categories.
The field of nonlinear dispersive waves has developed enormously since the work of Stokes, Boussinesq and Korteweg–de Vries (KdV) in the nineteenth century. In the 1960s, researchers developed effective asymptotic methods for deriving nonlinear wave equations, such as the KdV equation, governing a broad class of physical phenomena that admit special solutions including those commonly known as solitons. This book describes the underlying approximation techniques and methods for finding solutions to these and other equations. The concepts and methods covered include wave dispersion, asymptotic analysis, perturbation theory, the method of multiple scales, deep and shallow water waves, nonlinear optics including fiber optic communications, mode-locked lasers and dispersion-managed wave phenomena. Most chapters feature exercise sets, making the book suitable for advanced courses or for self-directed learning. Graduate students and researchers will find this an excellent entry to a thriving area at the intersection of applied mathematics, engineering and physical science.
Introduction To Nonlinear Dispersive Equations
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Author : Felipe Linares
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-02-21
Introduction To Nonlinear Dispersive Equations written by Felipe Linares 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 2009-02-21 with Mathematics categories.
The aim of this textbook is to introduce the theory of nonlinear dispersive equations to graduate students in a constructive way. The first three chapters are dedicated to preliminary material, such as Fourier transform, interpolation theory and Sobolev spaces. The authors then proceed to use the linear Schrodinger equation to describe properties enjoyed by general dispersive equations. This information is then used to treat local and global well-posedness for the semi-linear Schrodinger equations. The end of each chapter contains recent developments and open problems, as well as exercises.
Nonlinear Dispersive Equations
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Author : Terence Tao
language : en
Publisher: American Mathematical Soc.
Release Date :
Nonlinear Dispersive Equations written by Terence Tao 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 with Mathematics categories.
"Starting only with a basic knowledge of graduate real analysis and Fourier analysis, the text first presents basic nonlinear tools such as the bootstrap method and perturbation theory in the simpler context of nonlinear ODE, then introduces the harmonic analysis and geometric tools used to control linear dispersive PDE. These methods are then combined to study four model nonlinear dispersive equations. Through extensive exercises, diagrams, and informal discussion, the book gives a rigorous theoretical treatment of the material, the real-world intuition and heuristics that underlie the subject, as well as mentioning connections with other areas of PDE, harmonic analysis, and dynamical systems.".
Progress In Analysis And Its Applications Proceedings Of The 7th International Isaac Congress
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Author : Michael Ruzhansky
language : en
Publisher: World Scientific
Release Date : 2010-07-29
Progress In Analysis And Its Applications Proceedings Of The 7th International Isaac Congress written by Michael Ruzhansky and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-29 with Mathematics categories.
The International Society for Analysis, its Applications and Computation (ISAAC) has held its international congresses biennially since 1997. This proceedings volume reports on the progress in analysis, applications and computation in recent years as covered and discussed at the 7th ISAAC Congress. This volume includes papers on partial differential equations, function spaces, operator theory, integral transforms and equations, potential theory, complex analysis and generalizations, stochastic analysis, inverse problems, homogenization, continuum mechanics, mathematical biology and medicine. With over 500 participants from almost 60 countries attending the congress, the book comprises a broad selection of contributions in different topics.
Variable Lebesgue Spaces And Hyperbolic Systems
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Author : David Cruz-Uribe
language : en
Publisher: Springer
Release Date : 2014-07-22
Variable Lebesgue Spaces And Hyperbolic Systems written by David Cruz-Uribe and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-22 with Mathematics categories.
This book targets graduate students and researchers who want to learn about Lebesgue spaces and solutions to hyperbolic equations. It is divided into two parts. Part 1 provides an introduction to the theory of variable Lebesgue spaces: Banach function spaces like the classical Lebesgue spaces but with the constant exponent replaced by an exponent function. These spaces arise naturally from the study of partial differential equations and variational integrals with non-standard growth conditions. They have applications to electrorheological fluids in physics and to image reconstruction. After an introduction that sketches history and motivation, the authors develop the function space properties of variable Lebesgue spaces; proofs are modeled on the classical theory. Subsequently, the Hardy-Littlewood maximal operator is discussed. In the last chapter, other operators from harmonic analysis are considered, such as convolution operators and singular integrals. The text is mostly self-contained, with only some more technical proofs and background material omitted. Part 2 gives an overview of the asymptotic properties of solutions to hyperbolic equations and systems with time-dependent coefficients. First, an overview of known results is given for general scalar hyperbolic equations of higher order with constant coefficients. Then strongly hyperbolic systems with time-dependent coefficients are considered. A feature of the described approach is that oscillations in coefficients are allowed. Propagators for the Cauchy problems are constructed as oscillatory integrals by working in appropriate time-frequency symbol classes. A number of examples is considered and the sharpness of results is discussed. An exemplary treatment of dissipative terms shows how effective lower order terms can change asymptotic properties and thus complements the exposition.
Nonlinear Problems In Theoretical Physics
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Author : A. F. Ranada
language : en
Publisher: Springer
Release Date : 1979-06
Nonlinear Problems In Theoretical Physics written by A. F. Ranada and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979-06 with Science categories.
Journal Of Nonlinear Mathematical Physics
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Author :
language : en
Publisher: atlantis press
Release Date :
Journal Of Nonlinear Mathematical Physics written by and has been published by atlantis press this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.