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 1+1 and 2+1 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 $2A_{1}$, $A_{3,3}$ $\ $for the 1+1 generalized Zoomeron equation, and the $% A_{4,5}^{ab}\,$, $3A_{1}\otimes _{s}2A_{1}$ in the case of the 2+1 generalized Zoomeron equation. The one-dimensional optimal system is constructed for the two equations and similarity solutions are derived.\ The similarity transformation lead to the derivation of kink solutions. Indeed, the similarity exact solutions determined in this work are asymptotic solutions near to the singular behaviour of the kink behaviour.