The New Solitary Solutions to the Time-Fractional Coupled Jaulent–Miodek Equation

Abstract

Here, two applicable methods, namely, the tan θ / 2 -expansion technique and modified exp − θ ξ -expansion technique are being applied on the time-fractional coupled Jaulent–Miodek equation. Materials such as photovoltaic-photorefractive, polymer, and organic contain spatial solitons and optical nonlinearities, which can be identified by seeking from energy-dependent Schrödinger potential. Plentiful exact traveling wave solutions containing unknown values are constructed in the sense of trigonometric, hyperbolic, exponential, and rational functions. Different arbitrary constants acquired in the solutions help us to discuss the dynamical behavior of solutions. Moreover, the graphical representation of solutions is shown vigorously in order to visualize the behavior of the solutions acquired for the mentioned equation. We obtain some periodic, dark soliton, and singular-kink wave solutions which have considerably fortified the existing literature on the time-fractional coupled Jaulent–Miodek equation. Via three-dimensional plot, density plot, and two-dimensional plot by utilizing Maple software, the physical properties of these waves are explained very well.