  We examine the interaction of two-dimensional solitary pulses on falling
liquid films. We make use of the second-order model derived by Ruyer-Quil and
Manneville [Eur. Phys. J. B 6, 277 (1998); Eur. Phys. J. B 15, 357 (2000);
Phys. Fluids 14, 170 (2002)] by combining the long-wave approximation with a
weighted residuals technique. The model includes (second-order) viscous
dispersion effects which originate from the streamwise momentum equation and
tangential stress balance. These effects play a dispersive role that primarily
influences the shape of the capillary ripples in front of the solitary pulses.
We show that different physical parameters, such as surface tension and
viscosity, play a crucial role in the interaction between solitary pulses
giving rise eventually to the formation of bound states consisting of two or
more pulses separated by well-defined distances and travelling at the same
velocity. By developing a rigorous coherent-structure theory, we are able to
theoretically predict the pulse-separation distances for which bound states are
formed. Viscous dispersion affects the distances at which bound states are
observed. We show that the theory is in very good agreement with computations
of the second-order model. We also demonstrate that the presence of bound
states allows the film free surface to reach a self-organized state that can be
statistically described in terms of a gas of solitary waves separated by a
typical mean distance and characterized by a typical density.
