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Author | : Walter A. Strauss |
Publisher | : American Mathematical Soc. |
Total Pages | : 106 |
Release | : 1990-01-12 |
Genre | : Mathematics |
ISBN | : 0821807250 |
Download Nonlinear Wave Equations Book in PDF, ePub and Kindle
The theory of nonlinear wave equations in the absence of shocks began in the 1960s. Despite a great deal of recent activity in this area, some major issues remain unsolved, such as sharp conditions for the global existence of solutions with arbitrary initial data, and the global phase portrait in the presence of periodic solutions and traveling waves. This book, based on lectures presented by the author at George Mason University in January 1989, seeks to present the sharpest results to date in this area. The author surveys the fundamental qualitative properties of the solutions of nonlinear wave equations in the absence of boundaries and shocks. These properties include the existence and regularity of global solutions, strong and weak singularities, asymptotic properties, scattering theory and stability of solitary waves. Wave equations of hyperbolic, Schrodinger, and KdV type are discussed, as well as the Yang-Mills and the Vlasov-Maxwell equations. The book offers readers a broad overview of the field and an understanding of the most recent developments, as well as the status of some important unsolved problems. Intended for mathematicians and physicists interested in nonlinear waves, this book would be suitable as the basis for an advanced graduate-level course.
Author | : Jianke Yang |
Publisher | : SIAM |
Total Pages | : 452 |
Release | : 2010-12-02 |
Genre | : Science |
ISBN | : 0898717051 |
Download Nonlinear Waves in Integrable and Non-integrable Systems Book in PDF, ePub and Kindle
Nonlinear Waves in Integrable and Nonintegrable Systems presents cutting-edge developments in the theory and experiments of nonlinear waves. Its comprehensive coverage of analytical and numerical methods for nonintegrable systems is the first of its kind. This book is intended for researchers and graduate students working in applied mathematics and various physical subjects where nonlinear wave phenomena arise (such as nonlinear optics, Bose-Einstein condensates, and fluid dynamics).
Author | : Christopher Donald Sogge |
Publisher | : |
Total Pages | : 204 |
Release | : 2013 |
Genre | : Differential equations, Linear |
ISBN | : 9781571462794 |
Download Lectures on Non-linear Wave Equations Book in PDF, ePub and Kindle
Author | : Spencer P Kuo |
Publisher | : World Scientific |
Total Pages | : 206 |
Release | : 2021-04-16 |
Genre | : Science |
ISBN | : 9811231656 |
Download Linear And Nonlinear Wave Propagation Book in PDF, ePub and Kindle
Waves are essential phenomena in most scientific and engineering disciplines, such as electromagnetism and optics, and different mechanics including fluid, solid, structural, quantum, etc. They appear in linear and nonlinear systems. Some can be observed directly and others are not. The features of the waves are usually described by solutions to either linear or nonlinear partial differential equations, which are fundamental to the students and researchers.Generic equations, describing wave and pulse propagation in linear and nonlinear systems, are introduced and analyzed as initial/boundary value problems. These systems cover the general properties of non-dispersive and dispersive, uniform and non-uniform, with/without dissipations. Methods of analyses are introduced and illustrated with analytical solutions. Wave-wave and wave-particle interactions ascribed to the nonlinearity of media (such as plasma) are discussed in the final chapter.This interdisciplinary textbook is essential reading for anyone in above mentioned disciplines. It was prepared to provide students with an understanding of waves and methods of solving wave propagation problems. The presentation is self-contained and should be read without difficulty by those who have adequate preparation in classic mechanics. The selection of topics and the focus given to each provide essential materials for a lecturer to cover the bases in a linear/nonlinear wave course.
Author | : Roger K. Dodd |
Publisher | : |
Total Pages | : 630 |
Release | : 1982 |
Genre | : Science |
ISBN | : 9780122191220 |
Download Solitons and Nonlinear Wave Equations Book in PDF, ePub and Kindle
Author | : Satyanad Kichenassamy |
Publisher | : CRC Press |
Total Pages | : 297 |
Release | : 2021-05-30 |
Genre | : Mathematics |
ISBN | : 1000444724 |
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This work examines the mathematical aspects of nonlinear wave propagation, emphasizing nonlinear hyperbolic problems. It introduces the tools that are most effective for exploring the problems of local and global existence, singularity formation, and large-time behaviour of solutions, and for the study of perturbation methods.
Author | : Lokenath Debnath |
Publisher | : CUP Archive |
Total Pages | : 376 |
Release | : 1983-12-30 |
Genre | : Mathematics |
ISBN | : 9780521254687 |
Download Nonlinear Waves Book in PDF, ePub and Kindle
The outcome of a conference held in East Carolina University in June 1982, this book provides an account of developments in the theory and application of nonlinear waves in both fluids and plasmas. Twenty-two contributors from eight countries here cover all the main fields of research, including nonlinear water waves, K-dV equations, solitions and inverse scattering transforms, stability of solitary waves, resonant wave interactions, nonlinear evolution equations, nonlinear wave phenomena in plasmas, recurrence phenomena in nonlinear wave systems, and the structure and dynamics of envelope solitions in plasmas.
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 | : 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 | : 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.