Lie point symmetries, conservation laws and exact solutions of ($$1+ n$$)-dimensional modified Zakharov–Kuznetsov equation describing the waves in plasma physics

In this study, we explore the modified form of (\(1+n\))-dimensional Zakharov–Kuznetsov equation, which is used to investigate the waves in dusty and magnetised plasma. It is proved that the equation follows the property of nonlinear self-adjointness. Lie point symmetries are calculated and conservation laws in the framework of the new general conservation theorem of Ibragimov are obtained. The \((1/G^{\prime })\), \((G^{\prime }/G)\)-expansion and modified Kudryshov methods are applied to extract exact analytical solutions. The so-called bright, dark and singular solutions are also found using the solitary wave ansatz method. The results obtained in this study are new and may be of significant importance where this model is used to study the waves in different plasmas.