Diverse geometric shape solutions of the time-fractional nonlinear model used in communication engineering

Abstract

The nonlinear perturbed Radhakrishnan-Kundu-Lakshmanan (RKL) equation is a significant model in the engineering field for analyzing data transmission through nonlinear optical fibers. The two-variable (ψ′/ψ,1/ψ)-expansion method is a reliable scheme to compute self-controlled solitary wave solutions. In this study, we have constructed a wide range of geometric shapes and further inclusive soliton solutions comprising rational, trigonometric, and hyperbolic functions and their integration to the stated equation, devising the acknowledged method. The physical details of the ensued solitary wave solutions and the effects of fractional parameters are explained by sketching three- and two-dimensional graphs. For the appropriate values of the parameters, the periodic, V-shaped, bell-shaped, compacton, singular periodic, flat bell-shaped, plane-shaped, and some other types of solitons are formulated. The effect of the fractional derivative has been demonstrated by plotting the two-dimensional graphs for different values of the fractional order. It is important to note that changes in physical and auxiliary parameters cause variations in the wave profile. The formerly described physical phenomena may be better understood using the standard and new types of solitons. The results obtained exhibit the effectiveness, compatibility, and reliability of the two-variable (ψ′/ψ,1/ψ)-expansion approach for extracting soliton solutions of fractional-order nonlinear evolution equations in science, technology, and engineering.