Benjamin-Bona-Mahony (BBM) equation with variable coefficients: Similarity reductions and Painlevé analysis

The Lie-group formalism is applied to investigate the symmetries of the Benjamin-Bona-Mahony (BBM) equation with variable coefficients. We derive the infinitesimals and the admissible forms of the coefficients that admit the classical symmetry group. The ordinary differential equations deduced from the optimal system of subalgebras are further studied and some exact solutions are obtained.