Dynamics of Partial Differential Equations: 3 (Frontiers in Applied Dynamical Systems: Reviews and Tutorials, 3) - Softcover

Wayne, C. Eugene; Weinstein, Michael I.

Softcover

ISBN 10: 331919934X ISBN 13: 9783319199344

Publisher: Springer, 2015

Synopsis

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.

About this title

About the Author

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.

From the Back Cover

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.

Edition details

• Publisher: Springer
• Publication date: 2015
• Language: English
• ISBN 10: 331919934X
• ISBN 13: 9783319199344
• Binding: Paperback
• Edition number: 1
• Number of pages: 89