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.

Obtaining the Soliton Type Solutions of the Conformable Time-Fractional Complex Ginzburg–Landau Equation with Kerr Law Nonlinearity by Using Two Kinds of Kudryashov Methods

“…In literature, lots of researchers obtained the exact solutions of the given model with the diferent types of nonlinearity. Some researchers obtained the exact solutions of the generalized derivative of the given model for example Kudryashov applied the frst integral method to the equation in [14], Das et al applied the F-expansion to the model in [15], the modifed (G ′ /G)-expansion method is applied to the model by Wang et al in [16], the modifed Jacobi elliptic expansion method is applied by Hosseini et al in [17], Hosseini et al implemented Kudryashov and exponential methods to the model including the parabolic nonlinearity in [18]. Some researchers obtained the exact solutions of equation ( 1) with diferent kinds of fractional derivatives, for example, Tozar obtained the analytical solutions of the conformable time-fractional complex Ginzburg-Landau equation with the help of the (1/G ′ ) method in [19], optical solutions were discovered with the help of the generalized exponential rational function method in [20], Sulaiman et al explored the optical solitons with the help of the extended sinh-Gordon equation expansion method in [21], the form of the space-time conformable fractional complex Ginzburg-Landau equation is handled in [22], Sadaf et al applied the (w(ξ)/2) method to the model with the diferent types of senses as the conformable, beta, truncated derivatives in [23].…”

Soliton solutions of nonlinear (2 1)-dimensional Biswas-Milovic equation via new approach of generalized Kudryashov scheme

“…Optic wave propagation and optical soliton solution within the NLPD equations have also become the special focus of attention for researchers and have been a field of intense study. The perturbed NLSE in Kerr media, nonlinearities related to nonlinear Schrodinger equation (NLSE), Lakshmanan-Porsezian-Daniel equation, Manakov model, Triki-Biswas equation, Kaup-Newell equation, complex Ginzburg-Landau equation (CGLE), Kundu-Mukherjee-Naskar model, Sasa-Satsuma model, Chen-Lee-Liu model, Kundu-Eckhaus equation, Biswas-Milovic equation can be given as an example of the problems that have been studied intensively in optics recently [12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27].…”