We address the modulation instability of the Hirota equation in the presence of stochastic spatial incoherence and linear time-dependent amplification/attenuation processes via the Wigner function approach. We show that the modulation instability remains baseband type, though the damping mechanisms substantially reduce the unstable spectrum independent of the higher-order contributions (e.g. the higher-order nonlinear interaction and the third-order dispersion). Additionally, we find out that the unstable structure due to the Kerr interaction exhibits a significant resilience to the third-order-dispersion stabilizing effects in comparison with the higher-order nonlinearity, as well as a moderate Lorentzian spectrum damping may assist the rising of instability. Finally, we also discuss the relevance of our results in the context of current experiments exploring extreme wave events driven by the modulation instability (e.g. the generation of the so-called rogue waves).

我们通过维格纳函数方法解决了随机空间不相干和线性时间相关的放大/衰减过程中Hirota方程的调制不稳定性。我们显示出调制不稳定性仍然是基带类型，尽管阻尼机制大大降低了不稳定频谱，而不依赖于高阶贡献（例如，高阶非线性相互作用和三阶色散）。此外，我们发现，与高阶非线性相比，由于Kerr相互作用而导致的不稳定结构对三阶色散稳定效应表现出显着的弹性，适度的洛仑兹谱阻尼可能有助于增加不稳定性。 。最后，