A review of dispersive limits of (non)linear schrodinger-type equations

Ingenuin Gasser, Chi K. Lin, Peter Markowich

Veröffentlichungen: Beitrag in FachzeitschriftReviewPeer Reviewed

Abstract

In this review paper we present the most important mathematical properties of dispersive limits of (non)linear Schrošdinger type equations. Different formulations are used to study these singular limits, e.g., the kinetic formulation of the linear Schrošdinger equation based on the Wigner transform is well suited for global-in-time analysis without using WKB-(expansion) techniques, while the modified Madelung transformation reformulating Schrošdinger equations in terms of a dispersive perturbation of a quasilinear symmetric hyperbolic system usually only gives local-in-time results due to the hyperbolic nature of the limit equations. Deterministic analogues of turbulence are also discussed. There, turbulent diffusion appears naturally in the zero dispersion limit.
OriginalspracheEnglisch
Seiten (von - bis)501-529
Seitenumfang29
FachzeitschriftTaiwanese Journal of Mathematics
Jahrgang4
Ausgabenummer4
PublikationsstatusVeröffentlicht - 2000

ÖFOS 2012

  • 1010 Mathematik

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