Comments on: "Optical solitons in a parabolic law media with fourth order dispersion"[Appl. Math. Comput. 208(2009)209-302]

TL;DR

This paper critiques a previous study on optical solitons, identifies errors, and provides corrected analytical solutions including solitary and periodic waves using direct ansatz and F-expansion methods.

Contribution

It corrects errors in earlier work and introduces new analytical solutions for a fourth order dispersive nonlinear Schrödinger equation.

Findings

Identified mistakes in previous soliton solutions

Derived corrected solitary wave solutions of bell and kink shape

Presented periodic solutions using Jacobian elliptic functions

Abstract

Recently, Biswas and Milovic [Appl. Math. Comput. 208 (2009) 209-302] have found optical one-soliton solutions of a fourth order dispersive cubic-quintic nonlinear Schr\"odinger equation. In this comment, we first show there are mistakes in the paper and demonstrate that the obtained solutions do not satisfy the considered equation. And then we reconstruct a series of analytical exact solutions by means of a direct ansatz method and F-expansion method. These solutions include solitary wave solutions of the bell shape, solitary wave solutions of the kink shape, and periodic wave solutions of Jacobian elliptic function.