The K(m, n) equation with generalized evolution term studied by symmetry reductions and qualitative analysis

In this paper we obtain symmetry reductions of the K(m, n) equation with generalized evolution term. The reduction to ordinary differential equations comes from an optimal system of subalgebras. Some of these equations admit symmetries which lead to further reductions, and one of them comes out suitable for qualitative analysis. Its dynamical behavior is fully described and conservative quantities are stated.