Perturbed Fokas–Lenells equation: Lie symmetry analysis, complexitons and baseband modulation instability

Abstract

In this work, Lie symmetry analysis method is utilized to find the complex soliton solutions of the perturbed Fokas–Lenells equation. In this direction, first of all, we obtained the infinitesimals of the Fokas–Lenells equation with the help of the Lie symmetry method. After that, we reduced the Fokas–Lenells equation into the highly nonlinear system of an ordinary differential equation. Consequently, with the application of suitable back transformation, complex solitons are formulated for the Fokas–Lenells equation in trigonometric, hyperbolic and exponential functions. Finally, in this work, conditions of stability and instability are discussed with the aid of baseband modulation instability.