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

Advances in Difference Equations

Adil Jhangeer¹  Amjad Hussain²  Naseem Abbas²  Ilyas Khan³  El-Syed M. Sherif⁴ 

[1] Department of Mathematics, Namal Institute;Department of Mathematics, Quaid-I-Azam University;Faculty of Mathematics and Statistics, Ton DucThang University;Mechanical Engineering Department, College of Engineering, King Saud University;

关键词: Fractional complex Ginzburg–Landau equation;    New extended direct algebraic method;    Optical solitons;    Conformable derivative;    Beta derivative;    M-truncated derivative;   

DOI  :  10.1186/s13662-020-03052-7

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown