Lie symmetry classification for the 1+1 and 1+2 generalized Zoomeron equations

Abstract

We present a complete algebraic classification of the Lie symmetries for generalized Zoomeron equations. For the generalized [Formula: see text] and [Formula: see text] Zoomeron equations we solve the Lie symmetry conditions in order to constrain the free functions of the equations. We find that the differential equations of our consideration admit the same number of Lie symmetries with the non-generalized equations. The admitted Lie symmetries form the Lie algebras [Formula: see text], [Formula: see text] for the [Formula: see text] generalized Zoomeron equation, and the [Formula: see text], [Formula: see text] in the case of the [Formula: see text] generalized Zoomeron equation. The one-dimensional optimal system is constructed for the two equations and similarity solutions are derived. The similarity transformation led to the derivation of kink solutions. Indeed, the similarity exact solutions determined in this work are asymptotic solutions near the singular behavior of the kink behavior.