Dynamics of Nonlinear Waves in Dissipative Systems Reduction, Bifurcation and Stability: 1st Edition (Hardback) book cover

Dynamics of Nonlinear Waves in Dissipative Systems Reduction, Bifurcation and Stability

1st Edition

By G Dangelmayr, K Kirchgassner, B Fiedler, Alexander Mielke

Chapman and Hall/CRC

288 pages

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Hardback: 9780582229297
pub: 1996-08-01
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Description

The mathematical description of complex spatiotemporal behaviour observed in dissipative continuous systems is a major challenge for modern research in applied mathematics. While the behaviour of low-dimensional systems, governed by the dynamics of a finite number of modes is well understood, systems with large or unbounded spatial domains show intrinsic infinite-dimensional behaviour --not a priori accessible to the methods of finite dimensionaldynamical systems.

The purpose of the four contributions in this book is to present some recent and active lines of research in evolution equations posed in large or unbounded domains. One of the most prominent features of these systems is the propagation of various types of patterns in the form of waves, such as travelling and standing waves and pulses and fronts. Different approaches to studying these kinds of phenomena are discussed in the book. A major theme is the reduction of an original evolution equation in the form of a partial differential equation system to a simpler system of equations, either a system of ordinary differential equation or a canonical system of PDEs. The study of the reduced equations provides insight into the bifurcations from simple to more complicated solutions and their stabilities.

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Table of Contents

Introduction and Overview

Chapter 1 Ginzburg-Landau description of waves in extended systems, G Dangelmayr

Chapter 2 Global pathfollowing of homoclinic orbits in two-parameter flows, B Fiedler

Chapter 3 Stability of fronts for a KPP-system - the noncritical case, K Kirchg‰ssner and G Raugel

Chapter 4 A spatial center manifold approach to steady state bifurcations from spatially periodic patterns, A Mielke

References

About the Series

Chapman & Hall/CRC Research Notes in Mathematics Series

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Subject Categories

BISAC Subject Codes/Headings:
MAT003000
MATHEMATICS / Applied
MAT007000
MATHEMATICS / Differential Equations