Overview
- Third volume in Frontiers of Applied Dynamical Systems: Reviews and Tutorials series
- Contributions written by top international authors in the field
- Accessible and well written reviews of the areas
Part of the book series: Frontiers in Applied Dynamical Systems: Reviews and Tutorials (FIADS, volume 3)
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Table of contents (2 chapters)
Keywords
About this book
This book contains two review articles on the dynamics of partial differential equations that deal with closely related topics but can be read independently.
Wayne reviews recent results on the global dynamics of the two-dimensional Navier-Stokes equations. This system exhibits stable vortex solutions: the topic of Wayne's contribution is how solutions that start from arbitrary initial conditions evolve towards stable vortices. Weinstein considers the dynamics of localized states in nonlinear Schrodinger and Gross-Pitaevskii equations that describe many optical and quantum systems. In this contribution, Weinstein reviews recent bifurcations results of solitary waves, their linear and nonlinear stability properties and results about radiation damping where waves lose energy through radiation.
The articles, written independently, are combined into one volume to showcase the tools of dynamical systems theory at work in explaining qualitative phenomena associated with two classes of partial differential equations with very different physical origins and mathematical properties.
Reviews
“This third volume of ‘Reviews and Tutorials in Frontiers in Applied Dynamical Systems’ combines two review articles on unrelated topics. … Both review articles are written by experts in their fields. Therefore, many graduate students or young researchers may be interested to read these review articles to grasp the state-of-art in these areas of applications.” (Dmitry Pelinovsky, zbMATH 1331.35006, 2016)
Authors and Affiliations
About the authors
C.E. Wayne is a Professor in the Mathematics Department at Boston University. His research interests include dynamical systems, partial differential equations and mathematical physics.
M.I. Weinstein is a Professor of Applied Mathematics in the Department of Applied Physics and Applied Mathematics at Columbia University. His research interests include partial differential equations, applied analysis and dynamical systems.
Bibliographic Information
Book Title: Dynamics of Partial Differential Equations
Authors: C. Eugene Wayne, Michael I. Weinstein
Series Title: Frontiers in Applied Dynamical Systems: Reviews and Tutorials
DOI: https://doi.org/10.1007/978-3-319-19935-1
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2015
Softcover ISBN: 978-3-319-19934-4Published: 19 August 2015
eBook ISBN: 978-3-319-19935-1Published: 08 August 2015
Series ISSN: 2364-4532
Series E-ISSN: 2364-4931
Edition Number: 1
Number of Pages: X, 79
Number of Illustrations: 2 b/w illustrations, 12 illustrations in colour
Topics: Partial Differential Equations, Dynamical Systems and Ergodic Theory