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＜電子ブック＞
Dynamics of Partial Differential Equations / by C. Eugene Wayne, Michael I. Weinstein
(Frontiers in Applied Dynamical Systems: Reviews and Tutorials. ISSN:23644931 ; 3)

版	1st ed. 2015.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2015
大きさ	X, 79 p. 14 illus., 12 illus. in color : online resource
著者標目	*Wayne, C. Eugene author Weinstein, Michael I author SpringerLink (Online service)
件　名	LCSH:Differential equations LCSH:Dynamical systems FREE:Differential Equations FREE:Dynamical Systems
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-3-319-19935-1

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