Solitary wave solutions to a (3 + 1)-dimensional extended Zakharov–Kuznetsov model in a dusty magnetised plasma

This article studies the (3 + 1)-dimensional extended Zakharov–Kuznetsov (EZK) model describing the propagation of solitary waves across a magnetised dusty plasma. An analysis of the nonlinear three-dimensional dust-ion-acoustic solitary wave propagation in a magnetised two-ion-temperature dusty plasma is conducted. The sine–Gordon expansion method (SGEM) and \((1/{G}^{\prime})\) technique are implemented to discover new complex analytical solutions of the (3 + 1)-dimensional EZK model. These solutions comprise rational, exponential and hyperbolic functions. We plotted 3D, 2D and contour plots for some of the solutions for suitable parametric values. The graphs describe the change in the behaviour of solutions as values of free parameters are varied. All obtained solutions are checked using Maple software.