Rogue wave patterns of the Fokas-Lenells equation

Abstract In this work, we study the high-order rogue wave solution for the Fokas-Lenells equation 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 polynomials are the generalizations of the Yablonskii-Vorob'ev polynomial hierarchy, because of the arbitrariness of complex parameter . In addition, these rogue wave patterns are formed by the Peregrine solitons undergoing dilation, rotation, stretch, shear and translation. We also compare the prediction solutions with the corresponding true solutions and show the good consistency between them.