KPZ Equation and Surface Growth Model

We consider the ultra-discrete Burgers equation. All variables of the equation are discrete. We classify the equation into five regions in the parameter space. We discuss behavior of solutions. Using this equation we construct the deterministic surface growth models respectively. Furthermore we introduce noise into the ultra-discrete Burgers equation. We present the automata models of the KPZ equation. One model corresponds to the discrete version of the ASEP and the other to the Kim-Kosterlitz model.