Optical solitons to the Ginzburg–Landau equation including the parabolic nonlinearity

Abstract

The major goal of the present paper is to construct optical solitons of the Ginzburg-Landau (GL) equation including the parabolic nonlinearity. Such an ultimate goal is formally achieved with the aid of symbolic computation, a complex transformation, and Kudryashov and exponential methods. Several numerical simulations are given to explore the influence of the coefficients of nonlinear terms on the dynamical features of the obtained optical solitons. To the best of the authors' knowledge, the results reported in the current study, classified as bright and kink solitons, are new and have been acquired for the first time.

Dynamical perspective of bifurcation analysis and soliton solutions to (1+1)-dimensional nonlinear perturbed Schrödinger model

“…Step 2. The given assertion, using the given technique, clarifies the general solution for equation (4).…”

“…Lastly, use Wolfram Mathematica to solve the algebraic equation systems and get the values of the parameters. The solutions for equation (1) are obtained by substituting these values into equation (4). Accurate solutions to NLPDEs, such as the (1+1)-dimensional NLPSM, may be obtained with efficiency using the MSSEA.…”

“…These NLPDEs solutions provide improved support for the physical structures. To acquire the precise solution for nonlinear physical models, several robust and efficient techniques [4,5], were established, and these techniques are the Hirota bilinear technique [6], the F-expansion technique [7], the sinh-Gordon function technique [8], the Darboux transformation technique [9], new ϕ 6 -model expansion approach [10], the modified extended tanh-function technique [11,12], the sin-cosine technique [13] and several others. More recently, several approaches have also been considered for various lump solutions [14,15].…”

Investigation of optical soliton solutions for the perturbed Gerdjikov-Ivanov equation with full-nonlinearity

“…Moreover, in optic, there exist some phenomena equations that is based on NLSEs that describe an optical media or behavior like the optical propagation and fiber pulse propagation. Chen-Lee-Liu equation [24] , [25] , chiral NLSE [26] , Schrödinger-Hirota model [27] , Kundu-Eckhaus equation [28] , [29] , Sasa-Satsuma equation [30] , (1+1) dimensional perturbed NLSE [31] , Biswas-Milovic equation [32] , [33] , Ginzburg-Landau equation [34] , [35] , [36] and Kundu-Mukherjee-Naskar equation [37] can be briefly listed as major equations. To solve our model we used the computer algebra techniques.…”