Nondegenerate Akhmediev breathers arising from the instability of three-wave resonant interaction

We investigate the dynamics of nondegenerate Akhmediev breathers (ABs) in both the time and frequency domains within a three-wave resonant interaction system. In contrast to the conventional degenerate ABs, the nondegenerate ABs are composed of two fundamental ABs, each having an individual gain spectrum and exhibiting distinct structural configurations. We first presented the existence regions of degenerate and nondegenerate ABs, and then we numerically simulated the instability process of weak periodic perturbations on a plane wave and verified the results by integrating them with the exact AB solutions. Additionally, we provided a detailed explanation of the observed phenomena based on the instability analysis of the TWRI system.