A new family of traveling waves on falling films obtained in the limit of zero pulsing frequency is presented and analyzed. A new two-mode model that can describe the dynamics of waves for Weber numbers greater than unity is derived and validated. The speed (Ce) and peak height (h.) relation for solitary waves is predicted to be linear by the model and its predictions are in excellent agreement with experimental data. Weakly nonlinear analysis of the new wave family, using the new two-mode model, showed that the speed to peak height relation of these solitary waves is linear with slope root 3, which is in close agreement with experimental results. Furthermore, the local bifurcation analysis shows that the relation Ce - 3 = root 3(h(max) - 1) is independent of the angle of the inclination as well as fluid properties and flow rate. (c) 2006 American Institute of Chemical Engineers.