Rogue waves and their patterns for the coupled Fokas–Lenells equations.

In this work, we explore the rogue wave patterns in the coupled Fokas–Lenells equation by using the Darboux transformation. We demonstrate that when one of the internal parameters is large enough, the general high-order rogue wave solutions generated at a branch point of multiplicity three can be decomposed into some first-order outer rogue waves and a lower-order inner rogue wave. Remarkably, the positions and the orders of these outer and inner rogue waves are intimately related to Okamoto polynomial hierarchies. • A compact determinant formula of rogue wave solutions is constructed. • The rogue wave patterns are first derived with the aid of the Darboux transformation. • Some examples of rogue wave patterns are exhibited. [ABSTRACT FROM AUTHOR]