The dynamics of the modulation rogue waves in an inhomogeneous nonlinear optical fiber with the periodic modulation are studied. We find that for different modulation amplitudes and modulation frequencies, the modulation rogue wave solution can be Peregrine comb, rogue wave, or the transition state in between, respectively. In particular, the phase diagram of the three kinds of nonlinear states is given at the modulation amplitude and modulation frequency plane. Moreover, the dynamics characteristics of the Peregrine comb and the rogue wave are discussed on the localized soliton background. It is interesting that the main excitation characteristics of the Peregrine combs and the rogue waves on an infinitely wide plane wave background are well maintained on the soliton background. These results pave the way for exciting and manipulating the rogue waves on a local background.

研究了具有周期性调制的非均匀非线性光纤中调制流氓波的动力学。我们发现，对于不同的调制幅度和调制频率，调制无赖波解可以分别是百富勤梳，无赖波或两者之间的过渡状态。特别是，在调制幅度和调制频率平面上给出了三种非线性状态的相位图。此外，在局部孤子背景下讨论了百富勤梳和流浪波的动力学特性。有趣的是，在孤子背景上很好地保持了无限宽的平面波背景上的百富勤梳子和无赖波的主要激励特性。