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| Author | : Herbert Koch |
| Publisher | : Springer |
| Total Pages | : 310 |
| Release | : 2014-07-14 |
| Genre | : Mathematics |
| ISBN | : 3034807368 |
Download Dispersive Equations and Nonlinear Waves Book in PDF, ePub and Kindle
The first part of the book provides an introduction to key tools and techniques in dispersive equations: Strichartz estimates, bilinear estimates, modulation and adapted function spaces, with an application to the generalized Korteweg-de Vries equation and the Kadomtsev-Petviashvili equation. The energy-critical nonlinear Schrödinger equation, global solutions to the defocusing problem, and scattering are the focus of the second part. Using this concrete example, it walks the reader through the induction on energy technique, which has become the essential methodology for tackling large data critical problems. This includes refined/inverse Strichartz estimates, the existence and almost periodicity of minimal blow up solutions, and the development of long-time Strichartz inequalities. The third part describes wave and Schrödinger maps. Starting by building heuristics about multilinear estimates, it provides a detailed outline of this very active area of geometric/dispersive PDE. It focuses on concepts and ideas and should provide graduate students with a stepping stone to this exciting direction of research.
| Author | : Lokenath Debnath |
| Publisher | : World Scientific |
| Total Pages | : 683 |
| Release | : 1992-09-09 |
| Genre | : |
| ISBN | : 9814554960 |
Download Nonlinear Dispersive Wave Systems Book in PDF, ePub and Kindle
This book brings together a comprehensive account of major developments in the theory and applications of nonlinear dispersive waves, nonlinear water waves, KdV and nonlinear Schrodinger equations, Davey-Stewartson equation, Benjamin-Ono equation and nonlinear instability phenomena. In order to give the book a wider readership, chapters have been written by internationally known researchers who have made significant contributions to nonlinear waves and nonlinear instability. This volume will be invaluable to applied mathematicians, physicists, geophysicists, oceanographers, engineering scientists, and to anyone interested in nonlinear dynamics.
| Author | : G. B. Whitham |
| Publisher | : John Wiley & Sons |
| Total Pages | : 660 |
| Release | : 2011-10-18 |
| Genre | : Science |
| ISBN | : 1118031202 |
Download Linear and Nonlinear Waves Book in PDF, ePub and Kindle
Now in an accessible paperback edition, this classic work is just as relevant as when it first appeared in 1974, due to the increased use of nonlinear waves. It covers the behavior of waves in two parts, with the first part addressing hyperbolic waves and the second addressing dispersive waves. The mathematical principles are presented along with examples of specific cases in communications and specific physical fields, including flood waves in rivers, waves in glaciers, traffic flow, sonic booms, blast waves, and ocean waves from storms.
| Author | : P. L. Bhatnagar |
| Publisher | : Oxford University Press, USA |
| Total Pages | : 162 |
| Release | : 1979 |
| Genre | : Language Arts & Disciplines |
| ISBN | : |
Download Nonlinear Waves in One-dimensional Dispersive Systems Book in PDF, ePub and Kindle
| Author | : Mark J. Ablowitz |
| Publisher | : Cambridge University Press |
| Total Pages | : 363 |
| Release | : 2011-09-08 |
| Genre | : Mathematics |
| ISBN | : 1139503480 |
Download Nonlinear Dispersive Waves Book in PDF, ePub and Kindle
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.
| Author | : Jaime Angulo Pava |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 272 |
| Release | : 2009 |
| Genre | : Mathematics |
| ISBN | : 0821848976 |
Download Nonlinear Dispersive Equations Book in PDF, ePub and Kindle
This book provides a self-contained presentation of classical and new methods for studying wave phenomena that are related to the existence and stability of solitary and periodic travelling wave solutions for nonlinear dispersive evolution equations. Simplicity, concrete examples, and applications are emphasized throughout in order to make the material easily accessible. The list of classical nonlinear dispersive equations studied include Korteweg-de Vries, Benjamin-Ono, and Schrodinger equations. Many special Jacobian elliptic functions play a role in these examples. The author brings the reader to the forefront of knowledge about some aspects of the theory and motivates future developments in this fascinating and rapidly growing field. The book can be used as an instructive study guide as well as a reference by students and mature scientists interested in nonlinear wave phenomena.
| Author | : Carlos E. Kenig |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 177 |
| Release | : 2015-04-14 |
| Genre | : Mathematics |
| ISBN | : 1470420147 |
Download Lectures on the Energy Critical Nonlinear Wave Equation Book in PDF, ePub and Kindle
This monograph deals with recent advances in the study of the long-time asymptotics of large solutions to critical nonlinear dispersive equations. The first part of the monograph describes, in the context of the energy critical wave equation, the "concentration-compactness/rigidity theorem method" introduced by C. Kenig and F. Merle. This approach has become the canonical method for the study of the "global regularity and well-posedness" conjecture (defocusing case) and the "ground-state" conjecture (focusing case) in critical dispersive problems. The second part of the monograph describes the "channel of energy" method, introduced by T. Duyckaerts, C. Kenig, and F. Merle, to study soliton resolution for nonlinear wave equations. This culminates in a presentation of the proof of the soliton resolution conjecture, for the three-dimensional radial focusing energy critical wave equation. It is the intent that the results described in this book will be a model for what to strive for in the study of other nonlinear dispersive equations. A co-publication of the AMS and CBMS.
| Author | : Terence Tao |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 394 |
| Release | : 2006 |
| Genre | : Differential equations, Partial |
| ISBN | : 0821841432 |
Download Nonlinear Dispersive Equations Book in PDF, ePub and Kindle
"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.".
| Author | : Felipe Linares |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 263 |
| Release | : 2009-02-21 |
| Genre | : Mathematics |
| ISBN | : 0387848991 |
Download Introduction to Nonlinear Dispersive Equations Book in PDF, ePub and Kindle
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.
| Author | : Lokenath Debnath |
| Publisher | : World Scientific Publishing Company Incorporated |
| Total Pages | : 669 |
| Release | : 1992-01-01 |
| Genre | : Science |
| ISBN | : 9789810209483 |
Download Nonlinear Dispersive Wave Systems Book in PDF, ePub and Kindle
