Stability of moving Bragg solitons in a semilinear coupled system with cubic-quintic nonlinearity

We investigate the photonic bandgap structure, soliton properties and their stability in a semilinear coupled system where one core has cubic-quintic nonlinearity and is equipped with a Bragg grating, while the other one is uniform and linear. The investigation reveals that three distinct bandgaps, namely the upper, lower and central gaps, exist in the model. It is shown that the model supports two disjoint soliton families which are designated as Type 1 and Type 2 solitons. The soliton families exist only in the upper and lower bandgaps and are separated by a boundary at which no soliton solutions exist. A systematic numerical stability analysis is performed. It is found that vast regions in both the upper and lower bandgaps exist where Type 1 solitons are stable. However, Type 2 solitons are found to be always unstable. The effects of system parameters such as group velocity mismatch between the cores, velocity of solitons, and the coupling coefficient on the stability of solitons are analysed.