Stability and collisions of gap solitons in a model of a hollow optical fiber

We study soliton dynamics in a recently introduced model of two coupled waves propagating in a hollow-core fiber, which combines a linear dispersionless core mode and a dispersive nonlinear surface one (including the third-order dispersion). A bandgap opens in the system's spectrum due to the linear coupling between the modes. By computing the instability growth rate for the gap solitons filling the bandgap (both quiescent and moving ones), we demonstrate that, strictly speaking, all the solitons are subject to an oscillatory instability, but in a considerable part of the soliton family the instability is very weak, making that part virtually stable, which is corroborated by direct simulations. Collisions between moving solitons are studied too. It is found that collisions catalyze the destruction of unstable solitons, while practically stable ones collide elastically. The predicted solitons may be created in hollow-core photonic-crystal fibers.