Morphology and Scaling in the Noisy Burgers Equation: Soliton Approach to the Strong Coupling Fixed Point

The noisy Burgers equation in one dimension is treated by a nonlinear soliton approach based on the Martin-Siggia-Rose technique. In a canonical formulation the strong coupling fixed point is accessed by a principle of least action in the asymptotic nonperturbative weak noise limit. The scaling behavior and the growth morphology are described by a gas of solitons and a superposed gas of linear modes. The gapless soliton dispersion yields the dynamic exponent. The roughness exponent and the scaling function, of the form of a L\'evy distribution, follow from a spectral representation of the interface slope correlations.