Advances in Difference Equations | |
Optical solitons of fractional complex Ginzburg–Landau equation with conformable, beta, and M-truncated derivatives: a comparative study | |
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
【 预 览 】
Files | Size | Format | View |
---|---|---|---|
RO202104288011742ZK.pdf | 3392KB | download |