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

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

2004-12-21

arxiv.org/abs/physics/0412136v4

Physics

Plasma Physics

Scientific paper

We present a complete analytical resolution of the one dimensional Burgers equation with the elastic forcing term $-\kappa^{2} x+f(t)$, $\kappa\in\mathbb{R}$. Two methods existing for the case $\kappa=0$ are adapted and generalized using variable and function transformations, valid for all values of space an time. The emergence of a Fokker-Planck equation in the method allows to connect a fluid model, depicted by the Burgers equation, with an Ornstein-Uhlenbeck process.

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