Deformed and undeformed localized wave solutions for the two-component (2+1)-dimensional Fokas-Lenells equation

TL;DR

This paper develops a generalized Darboux transformation for the (2+1)-dimensional Fokas-Lenells equation, deriving various deformed and undeformed localized wave solutions, including rogue waves and breathers, highlighting the method's effectiveness.

Contribution

It introduces a determinant form of the Darboux transformation for the two-component (2+1)-D Fokas-Lenells equation and constructs a wide class of localized wave solutions.

Findings

Derived deformed solitons, positons, and breathers using DT.

Obtained higher-order rogue wave and breather-rogue wave solutions.

Showcased the efficiency of DT in multi-dimensional, multi-component systems.

Abstract

In this paper, we focus on the two-component (2+1)-dimensional Fokas-Lenells equation, which models the propagation of ultrashort optical pulses in nonlinear media with multi-mode interactions and multi-dimensional effects. Firstly, we construct the determinant form of the generalized Darboux transformation (DT). Secondly, we obtain deformed solitons, deformed positons on the zero background and deformed breathers, deformed Y-shaped breathers on the nonzero backgrounds by DT method. Finally, the undeformed solutions including higher-order rogue wave solutions and breather-rogue wave solutions are derived by generalized DT. This work enriches the solution family associated with the equation, but also illustrates the efficiency of DT method in multi-dimensional and multi-component systems.