Optical solitary wave and elliptic function solutions of the Fokas–Lenells equation in the presence of perturbation terms and its modulation instability

Abstract

In this paper, we study the Fokas–Lenells (F-L) equation in the presence of perturbation terms and we construct exact solutions. The modified extended direct algebraic method (MEDAM) is utilized, and soliton solutions, solitary wave solutions and elliptic function solutions are achieved. The physical meaning of the geometrical shapes for some of the obtained results is investigated for various choices of the free parameters that appear in the results. The stability of the model is investigated by using the standard linear stability analysis, which verifies that the exact solutions are stable. The achieved solutions and computational work show that the current method is powerful and influential.

Chirped optical soliton perturbation of Fokas–Lenells equation with full nonlinearity

“…The modulus of chirped bright soliton solution (28) is depicted in Fig. 5(a) Herein our target is to compare the results obtained here with corresponding results of some previous studies in the literature (e.g., [22][23][24][25][26][27][28][29][30][31]). The authors in [22,23], for instance, utilized the trial equation method and the complex envelope function ansatz to examine the combined solitary wave and chirped soliton solutions of the FL equation 1when perturbation terms are neglected (i.e., α = λ = μ = 0).…”

“…Also we mention the three methods of the modified Kudryashov's method, the exp(-ψ(η))-expansion method, and the sine-Gordon expansion method [26]. Finally, we have the semi-inverse variational principle [27], the Riccati equation method [28], the generalized exponential function method [29], the mapping method [30], the modified extended direct algebraic method [31], and the Laplace-Adomian decomposition method [32].…”

“…(1) represent inter-modal dispersion, self-steepening effect, and nonlinear dispersion, respectively. The authors in [23] investigated the chirped soliton solutions of the FL equation (1) in the absence of perturbation terms (i.e., α = λ = μ = 0) whereas the studies in [24][25][26][27][28][29][30][31][32] were devoted to the chirp-free soliton solutions of Eq. (1).…”

Bright-Dark and Multi Solitons Solutions of (3 + 1)-Dimensional Cubic-Quintic Complex Ginzburg–Landau Dynamical Equation with Applications and Stability

“…As numerical tools, the lattice Boltzmann method (LBM) has been broadly used in several study areas for examining fluid dynamics in the previous decade. The key theme behind using a lattice Boltzmann technique is to implement a straightforward mesoscopic equation of a fluid flow, generally concerning some distinct particle velocities that are not enough for describing properly the macroscopic flow pattern as the macroscopic PDEs are improved from the mesoscopic equation preserving preferred physical quantities and the principal to accurate fluxes of the preserved quantities [33][34][35]. Different self-interaction potentials were engineered in order to obtain nontrivial analytic results, with the purpose of testing the robustness of regarding the soliton as the ground state of the hairy sector, and its key role in the microscopic counting of hairy black hole entropy [36].…”

“…In recent years, NLSEs have attracted much attention from the constructing solitons and numerical solutions due to them being widely used to explain nonlinear complex phenomena. Several conventional techniques are extracted to obtain exact solutions such as the Tanh and Sech methods, the inverse scattering method, the extended tanh method, the Hirota bilinear and Darbox transform methods, the Bäcklund transform method, the generalized F-expansion technique, the Jacobi elliptic function expansion technique, the reduced differential transform method, the modified direct algebraic technique, variational iteration methods, and several others [28][29][30][31][32][33][34][35][37][38][39][40][41]. The authors in [40] have been working on CGLEs using different techniques like the modified simple equation method.…”