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A novel class of exact soliton solutions has been derived for the truncated M proportional modified mixed-Korteweg–de Vries (KdV) model, a mathematical physics model that elucidates the flat-topped electron distribution characterized by strong nonlinearity, resulting in a wave with narrower width and higher velocity. For our purpose, first we will convert the concerned model into corresponding ordinary differential equation by applying the wave transformation. Then we obtained the solutions by using the unified and modified simplest equation techniques, yielding results that include periodic, dark, kink, and many others. The influence of the derivatives was also explored. The soliton solutions are presented in two-dimensional (2D), three-dimensional (3D), and contour plots. The results have important applications in fluid dynamics, nonlinear optics, ocean engineering, and related fields. In addition, a stability analysis of the concerned equation was done, to confirm the stability of the considered equation as well as obtained results. At the end, it is demonstrated that the used techniques are simple as well as more effective for solving other nonlinear fractional models.

Novel exact solitons to the fractional modified mixed-Korteweg--de Vries model with a stability analysis