Uniqueness of travelling fronts for bistable nonlinear transport equations

We consider a nonlinear transport equation as a hyperbolic generalisation of the well-known reaction diffusion equation. Themodel is based on earlier work of K.P. Hadeler attempting to include run-and-tumble motion into the mathematical description. Previously, we proved the existence of strictly monotone travelling fronts for the three main types of the nonlinearity: the positive source term, the combustion law, and the bistable case. Here we revisit the latter case, showing that bistable fronts are unique up to translation.