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Inter-band Rabi oscillations of gap soliton matter waves induced by timedependent periodic forces in combined linear and nonlinear optical lattices arefor the first time demonstrated. It is shown that under suitable conditionsthese oscillations can become long-lived. By switching off the external forceat proper time it is possible to create either pure (stationary macroscopicallypopulated) gap soliton states or linear combination of two gap solitons withappreciably long life-time.

Rabi oscillations of matter wave solitons in optical lattices