<i>N</i>th-order breather and rogue wave solutions of the generalized Fokas–Lenells equation

Abstract A generalized Darboux transformation of the generalized Fokas-Lenells (GFL) equation is established in this paper. Starting from the plane wave seed solution, the analytical expression for the N th-order breather solutions of the GFL equation is derived by the classical Darboux transformation. Additionally, the N th-order rogue wave solutions of the GFL equation are obtained by the generalized Darboux transformation. To illustrate the dynamical properties of the obtained solutions, we present three-dimensional and density plots for the first- and second-order breather and rogue wave solutions by selecting appropriate parameters for visualization.