Dynamical analysis and localized waves of the <i>n</i>-component nonlinear Schrödinger equation with higher-order effects

Abstract Under investigation is the n -component nonlinear Schrödinger equation with higher-order effects, which describes the ultrashort pulses in the birefringent fiber. Based on the Lax pair, the eigenfunction and generalized Darboux transformation are derived. Next, we construct several novel higher-order localized waves and classified them into three categories: (i) higher-order rogue waves interacting with bright/antidark breathers, (ii) higher-order breather fission/fusion, (iii) higher-order breather interacting with soliton. Moreover, we explore the effects of parameters on the structure, collision process and energy distribution of localized waves and these characteristics are significantly different from previous ones. Finally, the dynamical properties of these solutions are discussed in detail.