# Solutions for a Generalized Type of the Fokas–Lenells Equation

## TL;DR

This paper studies a generalized version of the Fokas–Lenells equation and finds new exact solutions using the improved tanh–coth method.

## Contribution

The paper introduces novel soliton and chirped solutions for the Fokas–Lenells equation with variable coefficients.

## Key findings

- Exact solutions for the generalized Fokas–Lenells equation are derived using the improved tanh–coth method.
- Novel soliton and chirped solutions are obtained for the standard Fokas–Lenells equation.
- The behavior of solutions with variable coefficients reveals new structures and insights into the described phenomenon.

## Abstract

This work investigates the following generalization of the Fokas–Lenells equation. ıqt+A(t)qxx+B(t)qxt+C(t)|q|2q+ıD(t)|q|2qx=ı[H(t)qx+F(t)(|q|2q)x+G(t)(|q|2)xq] which is a Schro¨dinger-type equation with applications in theory of communications. Here, the coefficients are variables and depend on the temporal variable t. The improved tanh–coth method is used to obtain exact solutions for it in a general form. If the coefficients turn constants, the equation is known as the standard Fokas–Lenells equation (FLE) which has several applications in nonlinear science. As a particular case, novel soliton solutions, chirped solutions, and the respective chirps associated with them are derived for (FLE). Also, the work explores the behaviour of the solutions when the coefficients change in time, obtaining novel structures of the solutions which help understand in a better way the phenomenon described by the (FLE). We show the graphs of some of the solutions with the aim to compare the two cases, variable and constant coefficients. Finally, some conclusions are given.