Rogue waves and their patterns for the coupled Fokas-Lenells equations

TL;DR

This paper investigates the patterns of rogue waves in the coupled Fokas-Lenells equations using Darboux transformation, revealing their decomposition into simpler waves related to Okamoto polynomial hierarchies.

Contribution

It introduces a novel analysis of high-order rogue wave solutions, showing their decomposition and connection to polynomial hierarchies, advancing understanding of wave pattern structures.

Findings

High-order rogue waves decompose into first-order and lower-order waves.

Positions and orders of rogue waves relate to Okamoto polynomial hierarchies.

Large internal parameters influence rogue wave configurations.

Abstract

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.