Diverse chirped optical solitons and new complex traveling waves in nonlinear optical fibers

Abstract

This paper studies chirped optical solitons in nonlinear optical fibers. However, we obtain diverse soliton solutions and new chirped bright and dark solitons, trigonometric function solutions and rational solutions by adopting two formal integration methods. The obtained results take into account the different conditions set on the parameters of the nonlinear ordinary differential equation of the new extended direct algebraic equation method. These results are more general compared to Hadi et al (2018 Optik 172 545–53) and Yakada et al (2019 Optik 197 163108).

New shape of the chirped bright, dark optical solitons and complex solutions for (2+1) Ginzburg-Landau equation

“…This work addresses new shape of the chirped bright and dark soliton solutions through the CGLE by using the new sub-ODE equations. By using a special ansatz of the traveling wave transformation, we obtain a new shape of the chirp comparatively to the previous works reported in literature [26,[31][32][33][34]36,45]. In addition, new singular soliton solutions, trigonometric function solutions and complex traveling waves have been obtained.…”

“…These chirped pulses, have been widely investigated in diverse shape in recent years by [27][28][29]. From this, many results in theoretical and experimentally have been followed with the mathematical tools to handle them [10,35,36]. These analytical methods facilitated the success of these results are among others, the Sine-Gordon expansion method, the modifie exp(−ψ(ξ))expansion function method,(G'/G)-expansion scheme, the trial expansion method, the new mapping method, the auxiliary equation method, the rational function method, and the Riccati-Bernoulli sub-ODE method [25][26][27][28][29][30][35][36][37][38][39][40][41][42][43][44][45].…”

“…From this, many results in theoretical and experimentally have been followed with the mathematical tools to handle them [10,35,36]. These analytical methods facilitated the success of these results are among others, the Sine-Gordon expansion method, the modifie exp(−ψ(ξ))expansion function method,(G'/G)-expansion scheme, the trial expansion method, the new mapping method, the auxiliary equation method, the rational function method, and the Riccati-Bernoulli sub-ODE method [25][26][27][28][29][30][35][36][37][38][39][40][41][42][43][44][45]. In this present work, an investigation will be carried out in order to formulate new shape of the chirped soliton solutions to the famous (2+1)-dimensional complex Ginzburg-Landau equation (GLE), of which skeletal structure is as follows [29][30][31][32][33]:…”

New Solitary Wave Solutions for Variants of (3+1)-Dimensional Wazwaz-Benjamin-Bona-Mahony Equations

“…The solutions of (3) corresponding to (26), along with solution (10) are Case I: If c−k k µc > 0 and ρ = 0 then Case II: If c−k k µc < 0 and ρ = 0 then…”

“…Exact solutions produce corporal information to describe the physical behavior of system connected with these NLEs. In recent years, several efficient methods including method of extended tanh [1,2], tanh-coth [3,4], Hirota's direct [5,6], sine-cosine [7,8], extended direct algebraic [9,10], extended trial approach [11,12], Exp [-ϕ(ξ)]-Expansion [13,14], a new auxiliary equation [15,16], Jacobi elliptic ansatz [17,18], generalized Bernoulli sub-ODE [19,20], functional variable [21,22], sub equation [23,24], and so on [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39], have been established for efficient solutions of NLEs.…”