We propose the new, to the best of our knowledge, distributed mathematical model of dissipative soliton evolution in ultra-long fiber lasers. The model is based on a modified Ginzburg–Landau equation, has a stable analytical solution, and takes into account the saturated gain and saturable absorption. The analytical results show a good accordance with the results of numerical simulation of ultra-long ring cavity fiber lasers. The results may be applied to the analysis of a wide range of fiber laser systems.

中文翻译：

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超长锁模光纤激光器分布式数学模型中耗散孤子的研究

据我们所知，我们提出了超长光纤激光器中耗散孤子演化的新分布式数学模型。该模型基于修正的 Ginzburg-Landau 方程，具有稳定的解析解，并考虑了饱和增益和饱和吸收。解析结果与超长环腔光纤激光器的数值模拟结果吻合较好。结果可用于分析各种光纤激光系统。