Matched Optical Solitary Waves for 3-Level and 5-Level Systems

Exact analytic results are presented that give a general solution for a pair of solitary waves which can propagate through a three- and a five-level system with their shapes invariant. These solitary waves vary widely in shape and form: from ones for which the pulses have similar shape to ones which have very different but \u27\u27complementary\u27\u27 shapes. A general type of solitary-wave pair which is insensitive to small perturbations is identified