On the modified generalized multidimensional KP equation in plasma physics and fluid dynamics in (3+1) dimensions

Abstract

This paper considers a modified generalized multidimensional Kadomtsev–Petviashvili equation depending on several real constants, which characterizes the dynamics of solitons and the nonlinear waves in plasma physics and fluid dynamics. We derive the Lie point symmetry generators and Lie symmetry groups and we will apply this symmetry analysis to the equation in order to obtain exact solutions. Finally by means ot the multiplier method, we classify all low-order conservation laws of the equation that have been obtained by applying the corresponding symmetries of the family.