[Back]

A. Jüngel, R. Weishäupl:
"Blow -up in two-cpmponent nonlinear Schrödinger systems with an external driven field";
in: "ASC Report 33/2011", issued by: Institute of Analysis and Scientific Computing; Vienna University of Technology, Wien, 2011, ISBN: 978-3-902627-04-9.

A system of two nonlinear Schr¨odinger equations in up to three space dimensions is analyzed.
The equations are coupled through cubic mean-field terms and a linear term which
models an external driven field described by the Rabi frequency. The intraspecific meanfield
expressions may be non-cubic. The system models, for instance, two components of
a Bose-Einstein condensate in a harmonic trap. Sufficient conditions on the various model
parameters for global-in-time existence of strong solutions are given. Furthermore, the
finite-time blow-up of solutions is proved under suitable conditions on the parameters and
in the presence of at least one focusing nonlinearity. Numerical simulations in one and two
space dimensional equations verify and complement the theoretical results. It turns out
that the Rabi frequency of the driven field may be used to control the mass transport and
hence to influence the blow-up behavior of the system.

Nonlinear Schr¨odinger equations, global existence, blow-up of solutions,

http://www.asc.tuwien.ac.at/preprint/2011/asc33x2011.pdf