Degenerate fundamental nonlinear waves on the nonzero-zero background for a coupled Hirota system in a birefringent fiber

In this paper, we investigate a coupled Hirota system which models the wave propagation of two ultrashort optical fields in a birefringent fiber. Iterating the existing Darboux transformation at the same spectral parameter once and twice, we respectively construct the solutions to describe the so-called fundamental nonlinear waves (FNWs) and the degenerate FNWs. A two-branch condition is found to divide the FNWs into three-branch case and two-branch case. For the three-branch case, FNW is the nonlinear superposition of a breather and two dark-bright solitons, while for the two-branch case, FNW is the nonlinear superposition of a breather (not the Kuznetsov-Ma breather) and a dark-bright soliton. Compared with the degenerate nonlinear waves reported before, the degenerate three-branch FNW is found to obey the similar rule but the degenerate two-branch FNW not. Indeed, degenerate two-branch FNW is the nonlinear superposition of a breather, a dark-bright soliton and a two-branch FNW, and the trajectories of such three branches possess the same linear part but are not symmetric with respect to the common linear part. Thus, our study may offer a different point to explain certain phenomena observed in the optical experiments. Besides, we infer that our study can be generalized to the certain coupled systems which admit the similar nonlinear waves with the FNWs.