Shocks and excitations dynamics in a driven diffusive two-channel systems

We consider classical hard-core particles hopping stochastically on two parallel chains in the same or opposite directions with an inter- and intra-chain interaction. We discuss general questions concerning elementary excitations in these systems, shocks and rarefaction waves. From microscopical considerations we derive the collective velocities and shock stability conditions. The findings are confirmed by comparison to Monte Carlo data of a multi-parameter class of simple two lane driven diffusion models, which have the stationary state of a product form on a ring. Going to the hydrodynamic limit, we point out the analogy of our results to the ones known in the theory of differential equations of two conservation laws. We discuss the singularity problem and find a dissipative term that selects the physical solution