Plenty of accurate, explicit solitary unidirectional wave solutions of the nonlinear Gilson–Pickering model

Abstract

This paper proposes abundant accurate wave solutions that represent the plasma wave propagation based on crystal lattice theory and physicochemical characterization. The Gilson–Pickering ([Formula: see text]) model is analytically and numerically solved by two recent techniques. This model is a basic unidirectional wave propagation model that describes the prorogation of waves in crystal lattice theory and plasma physics. The investigated model has a deep connection with some nonlinear evolution equations under specific values of its parameters, such as the Fuchssteiner–Fokas–Camassa–Holm ([Formula: see text]) equation, the Rosenau–Hyman ([Formula: see text]) equation, and the Fornberg–Whitham ([Formula: see text]) equation. The Sardar sub-equation and He’s variational iteration techniques are employed to construct novel and accurate solitary wave solutions of the handled model. The obtained solutions are explained through some distinct graphs in contour, three-, two-dimensional. The research value is explained by comparing our results with some recently published studies. The employed methods show their simple, direct, effectiveness and their ability for handling many nonlinear evolution equations.