Dynamics of Partial Differential Equations electronic resource by C. Eugene Wayne, Michael I. Weinstein.
Material type: TextSeries: Frontiers in Applied Dynamical Systems: Reviews and TutorialsPublication details: Cham : Springer International Publishing : Imprint: Springer, 2015Edition: 1st ed. 2015Description: X, 79 p. 14 illus., 12 illus. in color. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783319199351Subject(s): mathematics | Dynamics | Ergodic theory | Partial Differential Equations | Mathematics | Partial Differential Equations | Dynamical Systems and Ergodic TheoryDDC classification: 515.353 LOC classification: QA370-380Online resources: Click here to access online In: Springer eBooksSummary: 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.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.
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