Similarity reductions and exact solutions of generalized Bretherton equation with time-dependent coefficients

In this paper, we apply Lie-group formalism to the generalized Bretherton equation with variable coefficients u (tt) +alpha(t)u (xx) +beta(t)u (xxxx) +delta(t)u (m) +theta(t)u (n) =0, to investigate the symmetries. 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.