Bragg grating solitons in semilinear dual-core system with cubic-quintic nonlinearity

The existence and stability of Bragg grating solitons in a coupler, where one core is equipped with a Bragg grating (BG) and has cubic-quintic nonlinearity and the other is linear, are studied. When the group velocity term in the linear core is zero (i.e. c = 0), the system's linear spectrum contains two separate bandgaps. It is found that soliton solutions exist throughout both bandgaps. On the other hand, when the group velocity term in the linear core is nonzero (c ≠ 0), the spectrum consists of three gaps: a genuine central gap and upper and lower gaps that overlap with one branch of continuous spectrum. In this case, soliton solutions exist throughout the upper and lower gaps but not in the central gap. The system supports two disjoint families of solitons (referred to as Type 1 and Type 2) that are separated by a boundary. Stability of solitons is investigated by means of systematic numerical stability analysis. It is found that Type 2 solitons are always unstable. On the other hand, there exist vast regions in the upper and lower bandgaps where stable Type 1 solitons exist.