We develop a method for transmission stabilization and robust dynamic switching for colliding optical soliton sequences in broadband waveguide systems with nonlinear gain and loss. The method is based on employing hybrid waveguides, consisting of spans with linear gain and cubic loss, and spans with linear loss, cubic gain, and quintic loss. We show that amplitude dynamics is described by a hybrid Lotka-Volterra (LV) model, and use the model to determine the physical parameter values required for enhanced transmission stabilization and switching. Numerical simulations with the coupled nonlinear Schrödinger equations confirm the predictions of the LV model, and show complete suppression of radiative instability, which enables stable transmission over distances larger by an order of magnitude compared with uniform waveguides with linear gain and cubic loss. Moreover, multiple on-off and off-on dynamic switching events are demonstrated over a wide range of soliton amplitudes, showing the superiority of hybrid waveguides compared with static switching in uniform waveguides. PACS numbers: 42.65.Tg, 42.81.Dp, 42.65.SfRecent years have seen a dramatic increase in research on broadband optical waveguide systems [1][2][3][4]. This increase in research efforts is driven by a wide range of applications, which include increasing transmission rates in fiber optics communication systems [2][3][4], enhancing data processing and transfer on computer chips [5][6][7][8], and enabling multiwavelength optical waveguide lasers [9][10][11][12][13][14]. Transmission in broadband systems is often based on wavelength-division-multiplexing (WDM), where many pulse sequences propagate through the same waveguide. The pulses in each sequence (each "frequency channel") propagate with the same group velocity, but the group velocity differs for pulses from different sequences.As a result, intersequence pulse collisions are very frequent, and can lead to severe transmission degradation [1,2,4,15,16]. On the other hand, the significant collision-induced effects can be used for controlling the propagation, for tuning of optical pulse parameters, such as energy, frequency, and phase, and for transmission switching, i.e., the turning on or off of transmission of one or more of the pulse sequences [17][18][19].One of the most important processes affecting pulse propagation in nonlinear waveguide systems is due to nonlinear loss or gain. Nonlinear loss (gain) can arise in optical waveguides due to multiphoton absorption (emission) or due to gain (loss) saturation [20,21]. For example, cubic loss due to two-photon absorption (TPA) plays a key role in pulse dynamics in a variety of waveguides, including silicon waveguides [5][6][7][8][22][23][24][25][26][27][28][29][30][31][32]. Furthermore, cubic gain and quintic loss are essential parts of the widely used Ginzburg-Landau (GL) model for pulse dynamics in mode-locked lasers [33][34][35][36][37][38]. The main effect of nonlinear loss (gain) on single pulse propagation is a continuous decrease (increase) o...