Transition mechanisms of breather molecules in the Hirota equation

The transition dynamics of the breather molecules are investigated for the Hirota equation, which describes the propagation of ultrashort optical pulses in optical fibers. Based on the two-breather solution, the breather molecules and breather complexes are obtained. The half-transition mechanism of the breather molecules is unveiled and a series of the transformed wave molecules and the corresponding complexes are generated. The superposition mechanisms of breather molecules and transformed wave molecules are explained through the nonlinear superposition principle. It should be noted that the full transition of the breather molecules does not exist in the Hirota equation. The effects of the phase parameters on the transformed wave molecules are discussed. Besides, the collisions for breather molecules and transformed wave molecules are investigated. The distances between atoms in the molecules and the shapes of the transformed waves are changed after the collisions. By means of the phase shift analysis, the nature of shape-changed collisions is shed light on. Finally, the stability of the propagation of molecule waves under small perturbations is performed.