Connection between the Burgers equation with an elastic forcing term and a stochastic process.

In this paper, a complete analytical resolution of the one dimensional Burgers equation with the elastic forcing term -k2x + f(t), k is an element of R is presented. Two methods existing for the case K=0 are adapted and generalized using variable and functional transformations, valid for all values of space and time. The emergence of a Fokker-Planck equation in the method allows the establishment of a connection between the Burgers equation and the Ornstein-Uhlenbeck process.