  We study collective phenomena of self-propagating particles using the
nonlinear Kramers equation. A solitary wave state appears from an instability
of the spatially uniform ordered state with nonzero average velocity. Two
solitary waves with different heights merge into a larger solitary wave. An
approximate solution of the solitary wave is constructed using a
self-consistent method. The phase transition to the solitary wave state is
either first-order or second-order, depending on the control parameters.
