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.
Highlights
The study of nonlinearity in physical phenomena is a well-established field of interest and its imperativeness is thought of through a sweer-amplitude wave oscillation investigated in various areas including plasma, chemical reactions, fluids, biological and solid states, to mention a few
4.1 Description of method we present the description of the new extended direct algebraic method [31, 37]
It is observed that for α = 1 and t = 1 all definitions have different structures, which was not the case for u1(x, t). 6 Conclusion In this study, we have used conformable, beta, and M-truncated derivatives to find the optical solitons of the fractional complex Ginzburg–Landau (CGL) equation with Kerr law
Summary
The study of nonlinearity in physical phenomena is a well-established field of interest and its imperativeness is thought of through a sweer-amplitude wave oscillation investigated in various areas including plasma, chemical reactions, fluids, biological and solid states, to mention a few. In this manner, the enthralling perspective in nonlinear physical phenomena are solitons. Hussain et al Advances in Difference Equations (2020) 2020:612 ous mechanisms These stimulated numerous specialists and researchers to concentrate on the establishments of solitons with optical structures with the assistance of different integration schemes [7, 8]
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