A vectorial Darboux transformation for integrable matrix versions of the Fokas–Lenells equation

Source abstract

Abstract Using bidifferential calculus, we derive a vectorial binary Darboux transformation for an integrable matrix version of the first negative flow of the Kaup–Newell hierarchy. A reduction from the latter system to an integrable matrix version of the Fokas–Lenells equation is then shown to inherit a corresponding vectorial Darboux transformation (DT). Matrix soliton solutions are derived from the trivial seed solution. Furthermore, the DT is exploited to determine in a systematic way exact solutions of the two-component vector Fokas–Lenells equation on a plane wave background. This comprises breathers, dark solitons, rogue waves and ‘beating solitons’.