The morphology and scaling properties of the noisy Burgers equation in one
dimension are treated by means of a nonlinear soliton approach based on the
Martin-Siggia-Rose technique. In a canonical formulation the strong coupling
fixed point is accessed by means of a principle of least action in the
asymptotic nonperturbative weak noise limit. The strong coupling scaling
behaviour and the growth morphology are described by a gas of nonlinear soliton
modes with a gapless dispersion law and a superposed gas of linear diffusive
modes with a gap. The dynamic exponent is determined by the gapless soliton
dispersion law, whereas the roughness exponent and a heuristic expression for
the scaling function are given by the form factor in a spectral representation
of the interface slope correlation function. The scaling function has the form
of a Levy flight distribution.Comment: 5 pages, Revtex file, submitted to Phys. Rev. Let