Localized waves and breather-to-soliton conversions of the coupled Fokas–Lenells system

Abstract

In this paper, we investigate the nonlinear localized waves on the plane wave backgrounds of the coupled Fokas–Lenells system, which models the ultrashort optical pulses in a birefringent optical fiber. By a given Darboux transformation, we obtain some nonlinear localized waves on the plane wave backgrounds, and provide the conversion conditions between the vector breathers and solitons. Velocities of the conversion solitons are only related to the dispersion condition and perturbation parameter. We exhibit the interaction mechanism, which results in the shape changed of the conversion solitons. The interactions of the vector breathers and rogue waves are presented through the semi-rational solutions.