Optical solitons of fractional complex Ginzburg–Landau equation with conformable, beta, and M-truncated derivatives: a comparative study

• Main Authors: Amjad Hussain, Adil Jhangeer, Naseem Abbas, Ilyas Khan, El-Syed M. Sherif
• Format: Article
• Language: English
• Published: SpringerOpen 2020-10-01
• Series: Advances in Difference Equations
• Subjects: Fractional complex Ginzburg–Landau equation; New extended direct algebraic method; Optical solitons; Conformable derivative; Beta derivative; M-truncated derivative
• Online Access: http://link.springer.com/article/10.1186/s13662-020-03052-7

Abstract In this paper, we investigate the optical solitons of the fractional complex Ginzburg–Landau equation (CGLE) with Kerr law nonlinearity which shows various phenomena in physics like nonlinear waves, second-order phase transition, superconductivity, superfluidity, liquid crystals, and strings in field theory. A comparative approach is practised between the three suggested definitions of derivative viz. conformable, beta, and M-truncated. We have constructed the optical solitons of the considered model with a new extended direct algebraic scheme. By utilization of this technique, obtained solutions carry a variety of new families including dark-bright, dark, dark-singular, and singular solutions of Type 1 and 2, and sufficient conditions for the existence of these structures are given. Further, graphical representations of the obtained solutions are depicted. A detailed comparison of solutions to the considered problem, obtained by using different definitions of derivatives, is reported as well.