SOLITON APPROACH TO THE NOISY BURGERS-EQUATION - STEEPEST DESCENT METHOD

The noisy Burgers equation in one spatial dimension is analyzed by mea ns of the Martin-Siggia-Rose technique in functional form. Ina canonic al formulation the morphology and scaling behavior are accessed by mea ns of a principle of least action in the asymptotic nonperturbative we ak noise limit. The ensuing coupled saddle point held equations for th e local slope and noise fields, replacing the noisy Burgers equation, are solved yielding nonlinear localized soliton solutions and extended linear diffusive mode solutions, describing the morphology of a growi ng interface. The canonical formalism and the principle of least actio n also associate momentum, energy, and action with a soliton-diffusive mode configuration and thus provide a selection criterion for the noi se-induced fluctuations. In a ''quantum mechanical'' representation of the path integral the noise fluctuations, corresponding to different paths in the path integral, are interpreted as ''quantum fluctuations' ' and the growth morphology represented by a Landau-type quasiparticle gas of ''quantum solitons'' with gapless dispersion E proportional to P-3/2 and ''quantum diffusive modes'' with a gap in the spectrum. Fin ally, the scaling properties are discussed from a heuristic point of v iew in terms of a ''quantum spectral representation'' for the slope co rrelations. The dynamic exponent z = 3/2 is given by the gapless solit on dispersion law, whereas the roughness exponent zeta = 1/2 follows f rom a regularity property of the form factor in the spectral represent ation. A heuristic expression for the scaling function is given by a s pectral representation and has a form similar to the probability distr ibution for Levy flights with index z.