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Morphology and scaling in the noisy Burgers equation: Soliton approach to the strong coupling fixed point

Hans C. Fogedby
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Abstract

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.

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BibTeXRIS

Hans C. Fogedby. 1997-09-04. Morphology and scaling in the noisy Burgers equation: Soliton approach to the strong coupling fixed point. https://doi.org/10.1103/physrevlett.80.1126

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