Microlocal Analysis And Nonlinear Waves
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Microlocal Analysis And Nonlinear Waves
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Author : Michael Beals
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Microlocal Analysis And Nonlinear Waves written by Michael Beals 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 2012-12-06 with Mathematics categories.
This IMA Volume in Mathematics and its Applications MICROLOCAL ANALYSIS AND NONLINEAR WAVES is based on the proceedings of a workshop which was an integral part of the 1988- 1989 IMA program on "Nonlinear Waves". We thank Michael Beals, Richard Melrose and Jeffrey Rauch for organizing the meeting and editing this proceedings volume. We also take this opportunity to thank the National Science Foundation whose financial support made the workshop possible. A vner Friedman Willard Miller, Jr. PREFACE Microlocal analysis is natural and very successful in the study of the propagation of linear hyperbolic waves. For example consider the initial value problem Pu = f E e'(RHd), supp f C {t ;::: O} u = 0 for t
Nonlinear Wave Equations
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Author : Tatsien Li
language : en
Publisher: Springer
Release Date : 2017-11-23
Nonlinear Wave Equations written by Tatsien Li and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-23 with Mathematics categories.
This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions and with all possible integer powers of nonlinear terms. Further, the book proposes the global iteration method, which offers a unified and straightforward approach for treating these kinds of problems. Purely based on the properties of solut ions to the corresponding linear problems, the method simply applies the contraction mapping principle.
Ray Methods For Nonlinear Waves In Fluids And Plasmas
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Author : Marcelo Anile
language : en
Publisher: CRC Press
Release Date : 2021-06-24
Ray Methods For Nonlinear Waves In Fluids And Plasmas written by Marcelo Anile and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-24 with Mathematics categories.
Presents in a systematic and unified manner the ray method, in its various forms, for studying nonlinear wave propagation in situations of physical interest, essentially fluid dynamics and plasma physics.
Nonlinear Waves A Geometrical Approach
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Author : Petar Radoev Popivanov
language : en
Publisher: World Scientific Publishing
Release Date : 2018-11-16
Nonlinear Waves A Geometrical Approach written by Petar Radoev Popivanov and has been published by World Scientific Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-16 with Mathematics categories.
This volume provides an in-depth treatment of several equations and systems of mathematical physics, describing the propagation and interaction of nonlinear waves as different modifications of these: the KdV equation, Fornberg-Whitham equation, Vakhnenko equation, Camassa-Holm equation, several versions of the NLS equation, Kaup-Kupershmidt equation, Boussinesq paradigm, and Manakov system, amongst others, as well as symmetrizable quasilinear hyperbolic systems arising in fluid dynamics.Readers not familiar with the complicated methods used in the theory of the equations of mathematical physics (functional analysis, harmonic analysis, spectral theory, topological methods, a priori estimates, conservation laws) can easily be acquainted here with different solutions of some nonlinear PDEs written in a sharp form (waves), with their geometrical visualization and their interpretation. In many cases, explicit solutions (waves) having specific physical interpretation (solitons, kinks, peakons, ovals, loops, rogue waves) are found and their interactions are studied and geometrically visualized. To do this, classical methods coming from the theory of ordinary differential equations, the dressing method, Hirota's direct method and the method of the simplest equation are introduced and applied. At the end, the paradifferential approach is used.This volume is self-contained and equipped with simple proofs. It contains many exercises and examples arising from the applications in mechanics, physics, optics and, quantum mechanics.
Nonlinear Waves
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Author : Peter R. Popivanov
language : en
Publisher: World Scientific
Release Date : 2011
Nonlinear Waves written by Peter R. Popivanov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
Big Nate is the star goalie of his school's soccer team, and he is tasked with defending his goal and saving the day against Jefferson Middle School, their archrival.
Nonlinear Wave Equations
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Author : Walter A. Strauss
language : en
Publisher: American Mathematical Soc.
Release Date : 1990-01-12
Nonlinear Wave Equations written by Walter A. Strauss 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 1990-01-12 with Mathematics categories.
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.
Nonlinear Wave Equations
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Author : Satyanad Kichenassamy
language : en
Publisher: CRC Press
Release Date : 2021-05-30
Nonlinear Wave Equations written by Satyanad Kichenassamy and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-30 with Mathematics categories.
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.
Symbolic Calculus Semilinear Hyperbolic Progressing Waves
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Author : Hassane Bougrini
language : en
Publisher: Nova Publishers
Release Date : 2000
Symbolic Calculus Semilinear Hyperbolic Progressing Waves written by Hassane Bougrini and has been published by Nova Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
The main purpose of this book is to give a self-contained synthesis of different results in the domain of symbolic calculus of conormal singularities of semilinear hyperbolic progressing waves. The authors deal generally with real matrix valued co-efficients and with real vector valued solutions, but the complex case is similar. They consider also N x N first order systems rather than high order scalar equations, because the polarisation properties of symbols are less natural in the latter case. Moreover, although they assume generally that the real characteristics are simple, the methods can give results for symmetric or symmetrisable first order hyperbolic systems.
Lectures On Nonlinear Hyperbolic Differential Equations
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Author : Lars Hörmander
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-07-17
Lectures On Nonlinear Hyperbolic Differential Equations written by Lars Hörmander 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 1997-07-17 with Mathematics categories.
In this introductory textbook, a revised and extended version of well-known lectures by L. Hörmander from 1986, four chapters are devoted to weak solutions of systems of conservation laws. Apart from that the book only studies classical solutions. Two chapters concern the existence of global solutions or estimates of the lifespan for solutions of nonlinear perturbations of the wave or Klein-Gordon equation with small initial data. Four chapters are devoted to microanalysis of the singularities of the solutions. This part assumes some familiarity with pseudodifferential operators which are standard in the theory of linear differential operators, but the extension to the more exotic classes of opertors needed in the nonlinear theory is presented in complete detail.
Third International Conference On Mathematical And Numerical Aspects Of Wave Propagation
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Author : Gary C. Cohen
language : en
Publisher: SIAM
Release Date : 1995-01-01
Third International Conference On Mathematical And Numerical Aspects Of Wave Propagation written by Gary C. Cohen and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-01-01 with Science categories.
This volume contains the papers presented at the title conference. Speakers from 13 different countries were represented at the meeting. A broad range of topics in theoretical and applied wave propagation is covered.