Abstract
We are interested in studying a Biswas-Milovic equation from various aspects. We prove that it does not have Painleve property, and hence, it is non-integrable in Painleve sense. Applying certain wave transformations, it turns to an ordinary differential equation which is equivalent to a Hamiltonian system. Based on the qualitative theorem of planar systems, we introduce the conditions that guarantee the existence of periodic, solitary and kink solutions for this equation in addition to some other singular solutions. The degeneracy of these solutions resulting from the transmission between the orbits is discussed. The 3D and 2D graphic representations for some wave solutions of this equation are presented beside the orbit relating to this solution.