The area theorems for two-core nonlinear directional couplers

The area theorems, describing propagation of ultrashort pulses of resonant laser radiation in a two-core nonlinear directional coupler, are formulated for the first time. It is shown that such a system is characterized by a finite, bounded above set of areas of the stationary propagating pulses. We also predict quantization of the limit cycles and possible existence of the regime of periodic complete transfer of the radiation energy from one fiber to another.