An investigation of fractional complex Ginzburg–Landau equation with Kerr law nonlinearity in the sense of conformable, beta and M-truncated derivatives

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

“…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].…”

Conservative Finite-Difference Scheme for 1D Ginzburg–Landau Equation

“…It is well known that the Ginzburg-Landau equation (GLE) was introduced in the scientific literature in the middle of the 20th century as a developing theory of superconductivity [1,2]. To date, the GLE has been widely used in the physics fields of superconductivity and superfluidity [3][4][5][6][7][8][9][10][11]. The GLE is used also for describing a number of nonlinear phenomena [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31], such as biophysics systems, nonlinear phenomena in liquid crystals, spatio-temporal chaos, oscillations of different nature (see review papers [32][33][34], where associated references can be found).…”