RETRACTED ARTICLE: Obtaining optical soliton solutions of the cubic–quartic Fokas–Lenells equation via three different analytical methods

Abstract

In this study, we have focused on finding soliton solutions of the cubic-quartic Fokas-Lenells equation, which models the nonlinear pulse transmission through optical fiber, is a pretty new and updated model. We have used three different efficient analytical methods, namely, the Sinh-Gordon expansion method, enhanced modified extended tanh expansion method and unified Riccati equation expansion method. By modifying our proposed method and using it effectively, we have obtained much more optical solutions. We have supported the results with the 3D surface, 2D and contour plots of the soliton solutions, such as singular, periodic, periodic-singular, dark and M-shaped solitons. The originality of the method we propose is that it has never been used before. With the innovation of the method, we have obtained M-shaped solitons, which are very rarely obtainable in soliton waves. On the other hand, enhanced modified extended tanh expansion method have provided us more extra solutions. As the last and most important part, in order to examine physical behaviors, we have investigated the effect of the coefficient of the fourth order dispersion parameter on wave propagation by presenting the graphical representation.

Fokas-Lenells equation dark soliton and gauge equivalent spin equation

“…Various methods, namely inverse scattering method, Hirota bilinearization and others (Lenells and Fokas, 2008;Matsuno, 2012b,a;Biswas et al, 2018b;Jawad et al, 2018;Krishnan et al, 2019;Biswas et al, 2018a;Aljohani et al, 2018;Onder et al, 2022;El-Shiekh and Hamdy, 2023;Gaballah et al, 2023;Cinar et al, 2022;Ullah et al, 2023) are proposed to obtain the different form of soliton solutions. In this manuscript our objective is to propose an alternate simplified and systematic scheme, namely bilinearization by introducing an auxiliary function and obtain a generalized expression for dark and bright dark soliton solutions.…”

Soliton Management for ultrashort pulse: dark and anti-dark solitons of Fokas-Lenells equation with a damping like perturbation and a gauge equivalent spin system

“…( 1) is relatively a new equation and the study on this is going on in full swing. Many analytical approaches have been employed to derive soliton solutions of FLE (Biswas et al, 2018;Hosseini et al, 2020;Triki and Wazwaz, 2017;Baronio et al, 2015;Chen et al, 2018;Cinar et al, 2022;Onder et al, 2022;Ullah et al, 2023;Gomez S et al, 2022;El-Shiekh and Hamdy, 2023;Gaballah et al, 2023;Krishnan et al, 2019;Matsuno, 2012b,a;Talukdar et al, 2023). In general the works on FLE is done for constant dispersion and nonlinear coefficients.…”

Soliton solutions of coupled resonant Davey-Stewartson system and modulation instability analysis

“…In the literature, there are some analytical methods used to obtain soliton solutions such as, enhanced modified extended tanh expansion method [14], Sardar sub-equation method [15], new Kudryashov method [16,17], extended rational sine-cosine and sinh-cosh method [18], generalized projective Riccati equation method [19], sinh-Gordon expansion method [20], generalized F-expansion method (GFEM) [21] and auxiliary equation method (AEM) [22].…”