On the nonlinear wave structures and stability analysis for the new generalized stochastic fractional potential-KdV model in dispersive medium

In this paper, the new generalized stochastic fractional potential-KdV model is investigated analytically which describes the nonlinear optical solitons and photons propagating in electric circuits and multicomponent plasmas. The governing model is transformed into a bilinear form using the Hirota bilinear method. A variety of novel waves structures are developed in the form of lump waves, collisions between lump waves and periodic waves, collisions between lump waves or single and double-kink soliton solutions, collisions between lump, periodic, single and double-kink soliton solutions. Furthermore, the ( \(G'/G^2\) $G^{\prime }/G^2$ ) expansion method and the Adomian decomposition method are employed to construct a number of new configurations for the governing dynamical model. To validate the scientific computations, a comparison study and stability analysis are carried out efficiently. Finally, to understand the dynamical behaviour of the the nonlinear fractional model, the 3D, 2D, and contour plots have also been demonstrated with the appropriate set of parameters. Depending upon the efficiency and the validity of the applied techniques, it is established that these strategies can also be applicable to many contemporary models.