Symmetry and singularity analyses of some equations of the fifth and sixth order in the spatial variable arising from the modelling of thin films

In the modelling of the flow of thin films higher-order derivatives in the spatial variable are introduced to model nonlinear effects. We examine nonlinear evolution equations of the fifth and sixth orders in the spatial variable from the viewpoint of Lie symmetry analysis. Values of the parameters which allow for a greater number of Lie point symmetries are identified. As the equations can be recast in potential form, we consider their potential symmetries. We also consider the singularity properties of the corresponding steady-state equations.