Abstract
We present a study of the effect of finite relaxation rates of media on the stability of dissipative solitons in single-mode fibers with longitudinal Bragg grating and nonlinear gain created by one active medium, and absorption created by one passive medium that gives the stability to solitons. The system of Maxwell–Bloch equations for this model is introduced. Based on the analysis of this system, it is shown that dissipative Bragg solitons are stable in the case when the active medium has greater relaxation rates than the passive medium.
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