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Deterministic Raman crosstalk effects in amplified wavelength division multiplexing transmission

We study the deterministic effects of Raman-induced crosstalk in amplified wavelength division multiplexing (WDM) optical fiber transmission lines. We show that the dynamics of pulse amplitudes in an N-channel transmission system is described by an N-dimensional predator-prey model. We find the equilibrium states with non-zero amplitudes and prove their stability by obtaining the Lyapunov function. The stability is independent of the exact details of the approximation for the Raman gain curve. Furthermore, we investigate the impact of cross phase modulation and Raman self and cross frequency shifts on the dynamics and establish the stability of the equilibrium state with respect to these perturbations. Our results provide a quantitative explanation for the robustness of differential-phase-shift-keyed WDM transmission against Raman crosstalk effects.