From scaling to multiscaling in the stochastic Burgers equation

We investigate the scaling behavior of the structure functions, [Formula Presented] in the stochastic Burgers equation as a function of the exponent β that characterizes the scale of noise correlations, for [Formula Presented] We analyze the exact equations satisfied by [Formula Presented] [Formula Presented] based on certain ansätze. For small negative β Kolmogorov-like scaling with [Formula Presented] is obtained; as [Formula Presented] an increasing multifractal structure occurs with bifractality for [Formula Presented] We determine [Formula Presented] and [Formula Presented] which are piecewise continuous and the associated multifractal scaling exponents.