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 Schršodinger 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 Schršodinger equations, global existence, blow-up of solutions,

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

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