Abstract
A system of two nonlinear Schrödinger 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.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
