Instabilities and Fronts in Extended Systems

Pierre Collet; Jean-Pierre Eckmann

Published by Princeton University Press 1990

Instabilities and Fronts in Extended Systems

Pierre Collet and Jean-Pierre Eckmann

Volume 50 in the series Princeton Series in Physics

In the series Princeton Legacy Library

https://doi.org/10.1515/9781400861026

Overview
Contents

About this book

The physics of extended systems is a topic of great interest for the experimentalist and the theoretician alike. There exists a large literature on this subject in which solutions, bifurcations, fronts, and the dynamical stability of these objects are discussed. To the uninitiated reader, the theoretical methods that lead to the various results often seem somewhat ad hoc, and it is not clear how to generalize them to the nextthat is, not yet solvedproblem. In an introduction to the subject of instabilities in spatially infinite systems, Pierre Collet and Jean-Pierre Eckmann aim to give a systematic account of these methods, and to work out the relevant features that make them operational. The book examines in detail a number of model equations from physics. The mathematical developments of the subject are based on bifurcation theory and on the theory of invariant manifolds. These are combined to give a coherent description of several problems in which instabilities occur, notably the Eckhaus instability and the formation of fronts in the Swift-Hohenberg equation. These phenomena can appear only in infinite systems, and this book breaks new ground as a systematic account of the mathematics connected with infinite space domains.

Originally published in 1990.

The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Topics

Frontmatter Publicly Available Download PDF	i
Contents Publicly Available Download PDF	v
Preface Requires Authentication Unlicensed Licensed Download PDF	ix
Outline Requires Authentication Unlicensed Licensed Download PDF	xi
CHAPTER I. SETTING THE STAGE Requires Authentication Unlicensed Licensed Download PDF	1
CHAPTER II. SMALL SOLUTIONS Requires Authentication Unlicensed Licensed Download PDF	17
CHAPTER III. BIFURCATION THEORY Requires Authentication Unlicensed Licensed Download PDF	31
CHAPTER IV. STATIONARY AND QUASISTATIONARY SOLUTIONS Requires Authentication Unlicensed Licensed Download PDF	59
CHAPTER V. CONSEQUENCES OF THE LINEAR INSTABILITY OF STATIONARY SOLUTIONS Requires Authentication Unlicensed Licensed Download PDF	91
CHAPTER VI. MULTISCALE ANALYSIS Requires Authentication Unlicensed Licensed Download PDF	127
CHAPTER VII. FRONTS Requires Authentication Unlicensed Licensed Download PDF	133
Outlook Requires Authentication Unlicensed Licensed Download PDF	183
Notation Requires Authentication Unlicensed Licensed Download PDF	187
Glossary Requires Authentication Unlicensed Licensed Download PDF	189
References Requires Authentication Unlicensed Licensed Download PDF	191
Analytical Index Requires Authentication Unlicensed Licensed Download PDF	195

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