We establish the existence and regularity properties of a monodromy operator for the linearization of the cubic–quintic complex Ginzburg–Landau equation about a periodically stationary (breather) solution. We derive a formula for the essential spectrum of the monodromy operator in terms of that of the associated asymptotic linear differential operator. This result is obtained using the theory of analytic semigroups under the assumption that the Ginzburg–Landau equation includes a spectral filtering (diffusion) term. We discuss applications to the stability of periodically stationary pulses in ultrafast fiber lasers.

中文翻译：

---

复金茨堡-朗道方程的周期平稳解的基本谱

我们建立了单峰算子的存在性和正则性，用于关于周期平稳（呼吸）解的三次-五次复数Ginzburg-Landau方程的线性化。我们根据相关的渐近线性微分算子得出了单峰算子基本谱的公式。假设Ginzburg-Landau方程包含一个光谱过滤（扩散）项，则使用解析半群理论获得此结果。我们讨论超快光纤激光器中周期性平稳脉冲的稳定性的应用。