New observation on the breather for a generalized nonlinear Schrödinger system with two higher-order dispersion operators in inhomogeneous optical fiber

A generalized nonlinear Schrödinger system is investigated, which can describe the soliton propagation in inhomogeneous optical fiber. The system comprises Lakshmanan–Porsezian–Daniel (LPD) operator with fourth-order dispersion and Hirota operator with third-order dispersion. Applying the Lax pair and generalized Darboux transformation technique, the breather solution is constructed for the system. The impacts of two operators on the breather propagation are discussed. The results show that these two operators can be used to govern the wave width, propagation direction, and rotation of every wave packet. However, LPD-operator has a stronger impact on the breather propagation. Furthermore, two types of breather structures are found, namely, the wave packet containing: (a) one peak and one trough, and (b) one peak and two troughs. The inherent parameter in the breather solution can be used to control the breather shifts between these two structures.