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, Talagang Road, 42250, Mianwali, Pakistan;Department of Mathematics, Quaid-I-Azam University, 45320, 44000, Islamabad, Pakistan;Faculty of Mathematics and Statistics, Ton DucThang University, 72915, Ho Chi Minh City, Vietnam;Mechanical Engineering Department, College of Engineering, King Saud University, P.O. Box 800, 11421, Al-Riyadh, Saudi Arabia;Electrochemistry and Corrosion Laboratory, Department of Physical Chemistry, National Research Centre, El-Buhouth, St. Dokki, 12622, Cairo, Egypt;

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: Springer

【 摘 要 】

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】

CC BY