Lectures On Nonlinear Waves And Shocks

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Lectures On Nonlinear Waves And Shocks

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Author : Cathleen S. Morawetz
language : en
Publisher:
Release Date : 1981

Lectures On Nonlinear Waves And Shocks written by Cathleen S. Morawetz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Gas dynamics categories.

Lectures On Nonlinear Waves And Shocks

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Author : Cathleen S. Morawetz
language : en
Publisher:
Release Date : 1981

Lectures On Nonlinear Waves And Shocks written by Cathleen S. Morawetz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Mathematics categories.

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.

Nonlinear Waves Hamiltonian Systems

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Author : Ricardo Carretero-González
language : en
Publisher: Oxford University Press
Release Date : 2024-11-05

Nonlinear Waves Hamiltonian Systems written by Ricardo Carretero-González and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-05 with Mathematics categories.

Nonlinear waves are of significant scientific interest across many diverse contexts, ranging from mathematics and physics to engineering, biosciences, chemistry, and finance. The study of nonlinear waves is relevant to Bose-Einstein condensates, the interaction of electromagnetic waves with matter, optical fibers and waveguides, acoustics, water waves, atmospheric and planetary scales, and even galaxy formation. The aim of this book is to provide a self-contained introduction to the continuously developing field of nonlinear waves, that offers the background, the basic ideas, and mathematical, as well as computational methods, while also presenting an overview of associated physical applications. Originated from the authors' own research activity in the field for almost three decades and shaped over many years of teaching on relevant courses, the primary purpose of this book is to serve as a textbook. However, the selection and exposition of the material will be useful to anyone who is curious to explore the fascinating world of nonlinear waves.

Rogue And Shock Waves In Nonlinear Dispersive Media

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Author : Miguel Onorato
language : en
Publisher: Springer
Release Date : 2016-09-19

Rogue And Shock Waves In Nonlinear Dispersive Media written by Miguel Onorato and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-19 with Science categories.

This self-contained set of lectures addresses a gap in the literature by providing a systematic link between the theoretical foundations of the subject matter and cutting-edge applications in both geophysical fluid dynamics and nonlinear optics. Rogue and shock waves are phenomena that may occur in the propagation of waves in any nonlinear dispersive medium. Accordingly, they have been observed in disparate settings – as ocean waves, in nonlinear optics, in Bose-Einstein condensates, and in plasmas. Rogue and dispersive shock waves are both characterized by the development of extremes: for the former, the wave amplitude becomes unusually large, while for the latter, gradients reach extreme values. Both aspects strongly influence the statistical properties of the wave propagation and are thus considered together here in terms of their underlying theoretical treatment. This book offers a self-contained graduate-level text intended as both an introduction and reference guide for a new generation of scientists working on rogue and shock wave phenomena across a broad range of fields in applied physics and geophysics.

Linear And Nonlinear Waves

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Author : G. B. Whitham
language : en
Publisher: Wiley-Interscience
Release Date : 1999-07

Linear And Nonlinear Waves written by G. B. Whitham and has been published by Wiley-Interscience this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-07 with Mathematics categories.

A Wiley-Interscience Series of Tests, Monographs, and Tracts.

Shock Waves And Reaction Diffusion Equations

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Author : Joel Smoller
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Shock Waves And Reaction Diffusion Equations written by Joel Smoller 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.

For this edition, a number of typographical errors and minor slip-ups have been corrected. In addition, following the persistent encouragement of Olga Oleinik, I have added a new chapter, Chapter 25, which I titled "Recent Results." This chapter is divided into four sections, and in these I have discussed what I consider to be some of the important developments which have come about since the writing of the first edition. Section I deals with reaction-diffusion equations, and in it are described both the work of C. Jones, on the stability of the travelling wave for the Fitz-Hugh-Nagumo equations, and symmetry-breaking bifurcations. Section II deals with some recent results in shock-wave theory. The main topics considered are L. Tartar's notion of compensated compactness, together with its application to pairs of conservation laws, and T.-P. Liu's work on the stability of viscous profiles for shock waves. In the next section, Conley's connection index and connection matrix are described; these general notions are useful in con structing travelling waves for systems of nonlinear equations. The final sec tion, Section IV, is devoted to the very recent results of C. Jones and R. Gardner, whereby they construct a general theory enabling them to locate the point spectrum of a wide class of linear operators which arise in stability problems for travelling waves. Their theory is general enough to be applica ble to many interesting reaction-diffusion systems.

Mathematics Of Complexity And Dynamical Systems

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Author : Robert A. Meyers
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-10-05

Mathematics Of Complexity And Dynamical Systems written by Robert A. Meyers 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 2011-10-05 with Mathematics categories.

Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.

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 Waves In Real Fluids

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Author : A. Kluwick
language : en
Publisher: Springer
Release Date : 2014-05-04

Nonlinear Waves In Real Fluids written by A. Kluwick and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-04 with Mathematics categories.

The study of materials which exhibit new and unconventional properties is of central importance for the devel- opment of advanced and refined technologies in many fields of engineering science. In this connection there has been a rapidly growing interest in real fluid effects on wave phenomena in the past few years. A prominent example is provided by Bethe-Zel'dovich-Thompson (BZT) fluids which have the distinguishing feature that they exhibit negative nonlinearity over a finite range of temperature and pressures in the pure vapour phase. However, two phase flows with and without phase change are an even richer source of new unexpected and previously thought impossible phenomena. Topics covered by this volume include waves in gases near the critical point, waves in retrograde fluids, temperature waves in superfluid helium and density waves in suspensions of particles in liquids. Clearly, the aim of the various contributions is twofold. First, they are intended to provide scientists and engineers working in these and related areas with an overview of various new physical phenomena as for example expansion shocks, sonic shocks, shock splitting, evaporation and liquafaction shocks and the experimental techniques needed to study these phenomena. Second, an attempt is made to discuss aspects of their mathematical modeling with special emphasis on properties which these phenomena have in common.