Optical solutions to the truncated M-fractional Schrödinger–KdV equation via an analytical method

Abstract

In this paper, we will use the exp \((-\Phi (\eta ))\) -expansion method to obtain the solitonic wave solution in the sense of the truncated M-fractional Schrödinger–KdV equation. The provided equation is converted into an ordinary differential equation using the appropriate wave transformation. Standard waveform shapes are determined, such as hyperbolic, exponential, dark, bright, rational, plane, and combo bright-dark soliton. We create 2D, density, and contour graphs of the solutions using consistent parametric values to examine the physical characteristics of the constructed solitons. Using Wolfram Mathematica, the newly created solutions are verified by inserting them back into the model under consideration. The suggested method and results can also be used to analyze high-order fractional models found in fields such as optics, hydrodynamics, plasma, wave theory, and others.