Rogue wave patterns of the Fokas-Lenells equation

In this work, we study the high-order rogue wave solution for the Fokas-Lenells equa-tion using the Kadomtsev-Petviashvili (KP) reduction method. These rogue wave patterns consist of triangle, pentagon, heptagon, nonagon, which are analytically described by the root structures of the Yablonskii-Vorob'ev polynomial hierarchy. On the other hand, we also report the other types of rogue wave patterns including heart-shaped, fan-shaped, two-arc+triangle, arc+pentagon, etc., which are analytically described by the root structures of Adler-Moser polynomials. These poly-nomials are the generalizations of the Yablonskii-Vorob'ev polynomial hierarchy, because of the arbitrariness of complex parameter a2j+1. In addition, these rogue wave patterns are formed by the Peregrine solitons undergoing dilation, rotation, stretch, shear and translation. We also com-pare the prediction solutions with the corresponding true solutions and show the good consistency between them.