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Dynamics of partial differential equ...

Wayne, C. Eugene, (1956-)

Dynamics of partial differential equations /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Dynamics of partial differential equations /C. Eugene Wayne, Michael I. Weinstein.
Author:	Wayne, C. Eugene,
other author:	Weinstein, Michael I.
Published:	Cham :Springer,c2015.
Description:	x, 79 p. :ill. (some col.) ;24 cm.
Subject:	Differential equations, Partial.
ISBN:	9783319199344 (pbk.) :

Dynamics of partial differential equations /
Wayne, C. Eugene,1956-

Dynamics of partial differential equations /C. Eugene Wayne, Michael I. Weinstein. - Cham :Springer,c2015. - x, 79 p. :ill. (some col.) ;24 cm. - Frontiers in applied dynamical systems: Reviews and tutorials,v. 32364-4532 ;. - Frontiers in applied dynamical systems ;v. 3..

Includes bibliographical references.

Dynamical systems and the two-dimensional Navier-Stokes equations /C. Eugene Wayne --Review 1.

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 Schrödinger/Gross-Pitaevskii equations that describe many optical and quantum systems. In this contribution, Weinstein reviews recent results on the bifurcation of solitary waves, their linear and nonlinear stability properties, and the role of radiation damping in the synamics of energy flow for the energy-conserving PDE. 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.

ISBN: 9783319199344 (pbk.) :NT$1222

LCCN: 2015942469Subjects--Topical Terms:

189753
Differential equations, Partial.

LC Class. No.: QA374 / .W39 2015

Dewey Class. No.: 515.3/53

Dynamics of partial differential equations /
LDR:02163cam a2200253 a 4500 001 465273
003 OCoLC
005 20151106022549.0
008 151217s2015 sz a b 000 0 eng d
010 $a 2015942469
020 $a 9783319199344 (pbk.) : $c NT$1222
020 $a 331919934X (pbk.)
020 $z 9783319199351 (eBook)
035 $a (OCoLC)908374378
035 $a 908374378
040 $a BTCTA $b eng $c BTCTA $d YDXCP $d CDX $d OCLCO $d OCLCF $d MUU
050 4 $a QA374 $b .W39 2015
082 0 4 $a 515.3/53 $2 23
100 1 $a Wayne, C. Eugene, $d 1956- $3 718919
245 1 0 $a Dynamics of partial differential equations / $c C. Eugene Wayne, Michael I. Weinstein.
260 $a Cham : $b Springer, $c c2015.
300 $a x, 79 p. : $b ill. (some col.) ; $c 24 cm.
490 1 $a Frontiers in applied dynamical systems: Reviews and tutorials, $x 2364-4532 ; $v v. 3
504 $a Includes bibliographical references.
505 0 0 $g Review 1. $t Dynamical systems and the two-dimensional Navier-Stokes equations / $r C. Eugene Wayne -- $g Review 2. $t Localized states and dynamics in the nonlinear Schrödinger/Gross-Pitaevskii equation / $r Michael I. Weinstein.
520 $a 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 Schrödinger/Gross-Pitaevskii equations that describe many optical and quantum systems. In this contribution, Weinstein reviews recent results on the bifurcation of solitary waves, their linear and nonlinear stability properties, and the role of radiation damping in the synamics of energy flow for the energy-conserving PDE. 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.
650 0 $a Differential equations, Partial. $3 189753
650 0 $a Schrödinger equation. $3 718922
650 0 $a Gross-Pitaevskii equations. $3 715984
700 1 $a Weinstein, Michael I. $3 718920
830 0 $a Frontiers in applied dynamical systems ; $v v. 3. $3 718921