Shock Structures and Velocity Fluctuations in the Noisy Burgers and KdV-Burgers Equations

Statistical properties of the noisy Burgers and KdV-Burgers equations are numerically studied. It is found that shock-like structures appear in the time-averaged patterns for the case of stepwise fixed boundary conditions. Our results show that the shock structure for the noisy KdV-Burgers equation has an oscillating tail, even for the time-averaged pattern. Also, we find that the width of the shock and the intensity of the velocity fluctuations in the shock region increase with system size.