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Dynamics of Partial Differential Equations [electronic resource] / by C. Eugene Wayne, Michael I. Weinstein

Author
Wayne, C. Eugene, 1956-
Published
Cham : Springer International Publishing : Imprint: Springer, 2015.
Edition
1st ed. 2015.
Physical Description
X, 79 pages 14 illustrations, 12 illustrations in color : online resource
Additional Creators
Weinstein, Michael I. and SpringerLink (Online service)
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Summary
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.
Subject(s)
ISBN
9783319199351
Digital File Characteristics
text file PDF
Note
AVAILABLE ONLINE TO AUTHORIZED PSU USERS.
Part Of
Springer eBooks
View MARC record | catkey: 16005675