New types of chirped soliton solutions for the Fokas–Lenells equation

Abstract

Purpose

The purpose of this paper is to present a reliable treatment of the Fokas–Lenells equation, an integrable generalization of the nonlinear Schrödinger equation. The authors use a special complex envelope traveling-wave solution to carry out the analysis. The study confirms the accuracy and efficiency of the used method.

Design/methodology/approach

The proposed technique, namely, the trial equation method, as presented in this work has been shown to be very efficient for solving nonlinear equations with spatio-temporal dispersion.

Findings

A class of chirped soliton-like solutions including bright, dark and kink solitons is derived. The associated chirp, including linear and nonlinear contributions, is also determined for each of these optical pulses. Parametric conditions for the existence of chirped soliton solutions are presented.

Research limitations/implications

The paper presents a new efficient algorithm for handling an integrable generalization of the nonlinear Schrödinger equation.

Practical/implications

The authors present a useful algorithm to handle nonlinear equations with spatial-temporal dispersion. The method is an effective method with promising results.

Social/implications

This is a newly examined model. A useful method is presented to offer a reliable treatment.

Originality/value

The paper presents a new efficient algorithm for handling an integrable generalization of the nonlinear Schrödinger equation.

Citation

Triki, H. and Wazwaz, A.-M. (2017), "New types of chirped soliton solutions for the Fokas–Lenells equation", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 27 No. 7, pp. 1596-1601. https://doi.org/10.1108/HFF-06-2016-0252