Conversions and interactions of the nonlinear waves in a generalized higher-order nonlinear Schrödinger equation

In this paper, we investigate a generalized higher-order nonlinear Schrödinger (NLS) equation with two free parameters, including the third-order and fourth-order dispersion with matching higher-order nonlinear effects. The results show that the breather solution can be converted into some types of localized and periodic waves under specified parameter conditions. Coupled with rich graphical examples, the coexistence and interaction of different nonlinear structures are displayed. Further, we demonstrate the explicit relation on the parallel propagation of the second-order breather solution.