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We demonstrate transmission stabilization against radiation emission byfrequency-dependent linear gain-loss and perturbation-induced frequencyshifting for solitons of the cubic-quintic nonlinear Schr\"odinger (CQNLS)equation. We consider soliton propagation in a nonlinear optical waveguide withfocusing cubic nonlinearity, defocusing quintic nonlinearity, and dissipativeperturbations due to weak frequency-dependent linear gain-loss, cubic loss, anddelayed Raman response. The frequency shifting is induced by delayed Ramanresponse. Our perturbation analysis and numerical simulations with theperturbed CQNLS equation show that transmission stabilization with CQNLSsolitons is indeed possible, and in this way provide the first demonstration ofthe stabilization method for solitons of a nonintegrable nonlinear wave model.Moreover, we find that transmission stabilization with energetic CQNLS solitonsis realized with significantly smaller frequency shifts and pulse distortioncompared with stabilization with energetic solitons of the cubic nonlinearSchr\"odinger equation. Therefore, our study also demonstrates thatstabilization of energetic solitons by the method is significantly improved bythe presence of defocusing quintic nonlinearity.

Stabilizing solitons of the cubic-quintic nonlinear Schr\"odinger equation by frequency-dependent linear gain-loss and delayed Raman response