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We study transmission stability and dynamics of pulse amplitudes in$N$-channel soliton-based optical waveguide systems, taking into accountsecond-order dispersion, Kerr nonlinearity, delayed Raman response, andfrequency dependent linear gain-loss. We carry out numerical simulations withsystems of $N$ coupled nonlinear Schr\"odinger (NLS) equations and compare theresults with the predictions of a simplified predator-prey model forRaman-induced amplitude dynamics. Coupled-NLS simulations for single-fibertransmission with $2 \le N \le 4$ frequency channels show stable oscillatorydynamics of soliton amplitudes at short-to-intermediate distances, in excellentagreement with the predator-prey model's predictions. However, at largerdistances, we observe transmission destabilization due to resonant formation ofradiative sidebands, which is caused by Kerr nonlinearity. The presence oflinear gain-loss in a single fiber leads to a limited increase in transmissionstability. Significantly stronger enhancement of transmission stability isachieved in a nonlinear $N$-waveguide coupler due to efficient suppression ofradiative sideband generation by the linear gain-loss. As a result, thedistances along which stable Raman-induced dynamics of soliton amplitudes isobserved are significantly larger in the waveguide coupler system compared withthe single-fiber system.

Transmission stability and Raman-induced amplitude dynamics in multichannel soliton-based optical waveguide systems