Local existence and WKB approximation of solutions to Schrödinger-Poisson system in the two-dimensional whole space

Details Local existence and WKB approximation of solutions to Schrödinger-Poisson system in the two-dimensional whole space Local existence and WKB approximation of solutions to Schrödinger-Poisson system in the two-dimensional whole space

2009-12-08

arxiv.org/abs/0912.1388v1

Mathematics

Analysis of PDEs

23 pages, no figure

Scientific paper

We consider the Schr\"odinger-Poisson system in the two-dimensional whole space. A new formula of solutions to the Poisson equation is used. Although the potential term solving the Poisson equation may grow at the spatial infinity, we show the unique existence of a time-local solution for data in the Sobolev spaces by an analysis of a quantum hydrodynamical system via a modified Madelung transform. This method has been used to justify the WKB approximation of solutions to several classes of nonlinear Schr\"odinger equation in the semiclassical limit.

Affiliated with

Also associated with

No associations

Rating

Local existence and WKB approximation of solutions to Schrödinger-Poisson system in the two-dimensional whole space does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Local existence and WKB approximation of solutions to Schrödinger-Poisson system in the two-dimensional whole space, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Local existence and WKB approximation of solutions to Schrödinger-Poisson system in the two-dimensional whole space will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-385317