A modified Davey–Stewartson system of nonlinear dust acoustic waves in (3+1) dimensions: Lie symmetries and exact solutions

This article is devoted to the analysis of a modified Davey–Stewartson system in three space dimensions, which was obtained in plasma physics for propagation of nonlinear dust acoustic waves. The system differs from the Davey–Stewartson systems available in the literature by an additional term which can be viewed as a constant complex potential. We show that, under a certain condition on the parameters of the system, this term can be removed by a transformation. This restriction also separates the different realizations of Lie symmetry algebra of the modified Davey–Stewartson system, which is identified as semi-direct sum of a finite-dimensional algebra with a Kac–Moody algebra. Having shed light on the group-theoretical properties of the system, we present several results on the exact solutions of generalized traveling wave type, some of which are line solitons and kink solitons on planes in space. We finalize by analyzing the stability of traveling wave solutions.