Computational modeling of wave propagation in plasma physics over the Gilson–Pickering equation

In this paper, the Gilson–Pickering equation is studied which enables a wave propagation in plasma physics and crystal lattice theory. Based on the auxiliary transformations, some sets of the nonlinear form of ODE along with some analytic solutions are derived. To study the characterizations of the new waves, the crystal lattice theory and plasma physics is studied by using the modified exponential Jacobi technique and generalized rational tan(ϕ/2)-expansion technique. Through the new approaches, some solitary solutions are proposed. Meanwhile, influence of the coefficients in that equation for the periodic and soliton is illustrated. The effect of the free variables on the solutions is investigated. The behavior of these solutions on qualitatively of different structural natures relying on physical parameters coefficients is analyzed. The reported bright explosive envelopes, explosive solitons, periodic blow up, bright periodic envelope and huge solitary waves are highly applied in plasma and nuclear physics, optical communications, electro-magnetic propagations, superfluid and plenty other applied sciences. For more details about the physical dynamical representation of the presented solutions, are illustrated with profile pictures using Mathematica and Matlab 18, to obtain complete configurations. The proposed approaches can be applied to several equations arising from all nonlinear applied sciences.