On similarity reductions and conservation laws of the two non-linearity terms‎ ‎Benjamin-Bona-Mahoney equation

‎In this paper‎, the Lie group of point symmetries for a‎ ‎kind of Benjamin-Bona-Mahoney (BBM) equation is obtained by applying the classical Lie‎ symmetry method‎. ‎An optimal system of sub-algebras of‎ ‎dimension one for the BBM equation is deduced by classifying the‎ ‎adjoint representation orbits of the Lie symmetry group‎. Then‎, ‎for any infinitesimal symmetry generators of the Lie group‎, ‎the related similarity reductions are generated‎. ‎Also‎, ‎new conservation laws for this equation are constructed by‎ ‎the method of scaling‎. ‎The conservation laws densities is calculated by using the concept‎ ‎of variables weight‎, ‎scaling symmetry and Euler operator‎ ‎and their fluxes is computed by applying the homotopy operator‎.