  The cooperative dynamics of a 1-D collection of Markov jump, interacting
stochastic processes is studied via a mean-field approach. In the
time-asymptotic regime, the resulting nonlinear master equation is analytically
solved. The nonlinearity compensates jumps induced diffusive behavior giving
rise to a soliton-like stationary probability density. The soliton velocity and
its sharpness both intimately depend on the interaction strength. Below a
critical threshold of the strength of interactions, the cooperative behavior
cannot be sustained leading to the destruction of the soliton-like solution.
The bifurcation point for this behavioral phase transition is explicitly
calculated.
