General rogue waves in the AB system

Abstract

In this work, general rogue wave solutions in the AB system are constructed by means of the Kadomtsev–Petviashvili hierarchy reduction method and explicit representations of these solutions are explored in terms of determinants whose matrix elements are fundamental Schur polynomials. Moreover, the dynamics of these rogue waves are investigated graphically by different choices of the free parameters. In particular, we observe that the rogue wave in the second component B is actually a four peaky-shaped rogue wave, different form the eye-shaped rogue wave in NLSE.