Darboux transformation and exact solutions for a four-component Fokas-Lenells equation

Abstract In the present paper, we introduce a 4 × 4 matrix spectral problem and derive a four-component Fokas-Lenells equation.  N -fold Darboux transformations for the four-component Fokas-Lenells equation are constructed by using the gauge transformation between spectral problems and an iterative procedure. Resorting to the limit technique and Taylor series, we obtain the  N -fold generalized Darboux transformation. As an illustrative example, by utilizing the resulting Darboux transformations and Mathematica software, some exact solutions for the four-component Fokas-Lenells equation are obtained, including solition, breather solution and rogue wave solution. Moreover, the dynamical behaviour of these solutions is analysed in detail.