Solitons in the noisy Burgers equation Original Research Article

The noisy Burgers equation describing the growth of an interface is analyzed in one dimension by means of the Martin–Siggia–Rose technique. In a canonical formulation the morphology and scaling behavior are accessed by a principle of least action in the weak noise limit. The growth morphology is characterized by a dilute gas of nonlinear soliton modes with gapless dispersion law E∝p3/2. The scaling exponents and a heuristic expression for the scaling function follow from a spectral representation.