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We present a complete algebraic classification of the Lie symmetries forgeneralized Zoomeron equations. For the generalized 1+1 and 2+1 Zoomeronequations we solve the Lie symmetry conditions in order to constrain the freefunctions of the equations. We find that the differential equations of ourconsideration admit the same number of Lie symmetries with the non-generalizedequations. 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 generalizedZoomeron equation. The one-dimensional optimal system is constructed for thetwo equations and similarity solutions are derived.\ The similaritytransformation lead to the derivation of kink solutions. Indeed, the similarityexact solutions determined in this work are asymptotic solutions near to thesingular behaviour of the kink behaviour.

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