Comment on ``Connection between the Burgers equation with an elastic forcing term and a stochastic process''

TL;DR

This paper clarifies that the previously claimed connection between the Burgers equation with elastic forcing and the Ornstein-Uhlenbeck process is only valid for the repulsive case, correcting a prior misconception.

Contribution

It corrects a prior claim by showing the connection holds only for the repulsive forcing, not the elastic case.

Findings

The connection between Burgers equation and Ornstein-Uhlenbeck process is limited to repulsive forcing.

The elastic forcing case does not correspond to the Ornstein-Uhlenbeck process.

Clarifies the conditions under which the connection is valid.

Abstract

In the above mentioned paper by E. Moreau and O. Vall\'{e}e [Phys. Rev. {\bf E 73}, 016112, (2006)], the one-dimensional Burgers equation with an elastic (attractive) forcing term has been claimed to be connected with the Ornstein-Uhlenbeck process. We point out that this connection is valid only in case of the repulsive forcing.