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The Stochastic Burger's Equation in Ito's Sense

We consider the solution to Burger's equation coupled to a stochastic noise in Ito's sense. The main random properties of the wave are determined. The solution is related to a deterministic problem with a rescaled diffusion coefficient. Depending on the value of a parameter, the initial value problem may be ill posed, well posed up to an explosion time, or well posed for all time. Traveling waves are destroyed asymptotically by white noise. However, the only effect of colored noise is to render the wave position random.