Semiclassical regularization of Vlasov equations and wavepackets for nonlinear Schrödinger equations

Content Provider	Scilit
Author	Athanassoulis, Agissilaos
Copyright Year	2018
Description	Journal: Nonlinearity We consider the semiclassical limit of nonlinear Schrödinger equations with initial data that are well localized in both position and momentum (non-parametric wavepackets). We recover the Wigner measure (WM) of the problem, a macroscopic phase-space density which controls the propagation of the physical observables such as mass, energy and momentum. WMs have been used to create effective models for wave propagation in: random media, quantum molecular dynamics, mean field limits, and the propagation of electrons in graphene. In nonlinear settings, the Vlasov-type equations obtained for the WM are often ill-posed on the physically interesting spaces of initial data. In this paper we are able to select the measure-valued solution of the 1 + 1 dimensional Vlasov–Poisson equation which correctly captures the semiclassical limit, thus finally resolving the non-uniqueness in the seminal result of Zhang et al (2012 Comm. Pure Appl. Math. 55 582–632). The same approach is also applied to the Vlasov–Dirac–Benney equation with small wavepacket initial data, extending several known results.
Related Links	http://arxiv.org/pdf/1505.04707 http://iopscience.iop.org/article/10.1088/1361-6544/aa9a86/pdf
Ending Page	1072
Page Count	28
Starting Page	1045
ISSN	09517715
e-ISSN	13616544
DOI	10.1088/1361-6544/aa9a86
Journal	Nonlinearity
Issue Number	3
Volume Number	31
Language	English
Publisher	IOP Publishing
Publisher Date	2018-02-12
Access Restriction	Open
Subject Keyword	Journal: Nonlinearity Mathematical Physics Semiclassical Limit
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Statistical and Nonlinear Physics Mathematical Physics