We present results from extensive numerical integration of the Kardar-Parisi-Zhang (KPZ) equation in $1+1$ dimensions aimed to check the long-time behavior of the dynamical structure factor of that system. Over a number of decades in the size of the structure factor we confirm scaling and stretched exponential decay. We also give an analytic expression that yields a very good approximation to the numerical data. Our result clearly favors stretched exponential decay over recent results claiming to yield the exact time dependent structure factor of the $1+1$-dimensional KPZ system. We suggest a possible solution to that contradiction.

• Received 23 October 2003

DOI:https://doi.org/10.1103/PhysRevE.69.052603