Vector rational and semi-rational rogue waves for the coupled cubic-quintic nonlinear Schr??dinger system in a non-Kerr medium

摘要： Non-Kerr media possess certain applications in photonic lattices and optical fibers. Studied in this paper are the vector rational and semi-rational rogue waves in a non-Kerr medium, through the coupled cubic-quintic nonlinear Schr?dinger system, which describes the effects of quintic nonlinearity on the ultrashort optical pulse propagation in the medium. Applying the gauge transformations, we derive the N th-order Darboux transformtion and N th-order vector rational and semi-rational rogue wave solutions, where N is a positive integer. With such solutions, we present three types of the second-order rogue waves with the triangle structure: the one with each component containing three four-petalled rogue waves, the one with each component containing three eye-shaped rogue waves, and the other with one component containing three anti-eye-shaped rogue waves and the other component containing three eye-shaped rogue waves. We exhibit the third-order vector rogue waves with the merged, triangle and pentagon structures in each component. Moreover, we show the first- and second-order vector semi-rational rogue waves which display the coexistence of the rogue waves and the breathers.