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A. Jüngel, R. Weishäupl:
"Blow-up in two-component nonlinear Schrödinger systems with an external driven field";
Mathematical Models & Methods in Applied Sciences, 23 (2013), 9; S. 1699 - 1727.

Siehe englisches Abstract.

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
mean-field 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 dimensions 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.

Schrödinger equation; Bose-Einstein condensate

http://dx.doi.org/10.1142/S0218202513500206