Discovery of exact solitons to the fractional KP-MEW equation with stability analysis

Abstract

This research derives the new solitons for the fluid wave model, a nonlinear Kadomtsev–Petviashvili-modified equal width model along truncated M-fractional derivative. Our concerned model is utilized to explain the matter-wave pulses, waves in ferromagnetic media, and long wavelength water waves with frequency dispersion and faintly nonlinear reinstating forces, and others. To this end, we apply the modified extended direct algebraic and the improved \((G'/G)\)-expansion techniques. Fractional transformation is utilized to convert the nonlinear fractional partial differential equation into a nonlinear ordinary differential equation. Mathematica software is used to gain the solutions, verify them, and demonstrate them in two-, three-dimensional, and contour plots. The impact of fractional derivative is represented through two-dimensional plot. A linear stability process is conducted to confirm that governing equation is stable. The techniques are reliable to use and provide the various types of solutions.