WSEAS Transactions on Systems and Control
Print ISSN: 1991-8763, E-ISSN: 2224-2856
Volume 18, 2023
Exact Solutions of the Paraxial Wave Dynamical Model in Kerr Media with Truncated M-fractional Derivative using the (G′/G, 1/G)-Expansion Method
Authors: , , ,
Abstract: The main purpose of this article is to use the (G′/G, 1/G)-expansion method to derive exact traveling
wave solutions of the paraxial wave dynamical model in Kerr media in the sense of the truncated M-fractional
derivative. To the best of the authors’ knowledge, the solutions of the model obtained using the expansion method
are reported here for the first time. The exact solutions are complex-valued functions expressed in terms of
hyperbolic, trigonometric, and rational functions. In order to show the physical interpretations of the solutions,
the magnitude of selected solutions is plotted in 3D, 2D, and contour plots for a range of values of the fractionalorder
of the equation. With the aid of a symbolic software package, all of the obtained solutions are substituted
back into the relevant equation to verify their correctness. Obtaining the results by this technique confirms the
strength and efficacy of the method for generating a variety of exact solutions of the problems arising in applied
sciences and engineering.
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Keywords: Exact solutions, Paraxial wave dynamical model, Kerr media, (G′/G, 1/G)-expansion method,
Truncated M-fractional derivative, Anti-soliton solution
Pages: 498-512
DOI: 10.37394/23203.2023.18.53