Fig. 1. Dynamics distributions of fundamental breathers

Fig. 2. Amplitude distributions of Kuznestov-Ma breather in time and frequency domain

Fig. 3. Amplitude distributions of Akhmediev breather in time and frequency domain

Fig. 4. Amplitude distributions of Peregrine rogue wave in time and frequency domain

Fig. 5. Random perturbation excitation on a broadband noise background^［1］

Fig. 6. MI distributions and phase diagrams of fundamental breathers in NLS system

Fig. 7. Conversion relationship between breathers and Peregrine rogue waves

Fig. 8. Dynamics of collision interactions between two ABs^{［22，56］}

Fig. 9. Dynamics of quasi-annihilation interactions between two breathers^{［23，54］}

Fig. 10. Dynamics of ghost interactions between two breathers^［55］