Characteristics of solitary waves on a running film down an inclined plane under an electrostatic field

For the study on the nonlinear dynamics of thin-film flow running down an inclined plane under the effect of an electrostatic field, the mechanism of solitary waves has been examined by using a global bifurcation theory. First, the existence of solitary waves has been chased by using an orbit homoclinic to a fixed point of saddle-focus type in a linearized third-order ordinary differential equation which resulted from the evolution equation in a steady moving frame. Then, the trajectories with several kinds of solitary waves have also been searched numerically for the nonlinear system. In addition, the behavior of these waves has been directly confirmed by integrating the initial-value problem. The slightly perturbed waves at the inception eventually evolve downstream into almost permanent pulse-like solitary waves through the processes of coalescence and repulsion of the triggered subharmonics. In the global aspects the flow system at a given Reynolds number becomes more unstable and chaotic than when there is no electrostatic force applied.