Scaling function for the noisy Burgers equation in the soliton approximation

Abstract

We derive the scaling function for the one dimensional noisy Burgers equation in the two-soliton approximation within the weak noise canonical phase space approach. The result is in agreement with an earlier heuristic expression and exhibits the correct scaling properties. The calculation presents the first step in a many body treatment of the correlations in the Burgers equation.

Replacement: Several corrections, 4 pages, Revtex file, 3 figures. To appear in Europhysics Letters

References in corpus (4)

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• Upper critical dimension, dynamic exponent and scaling functions in the mode-coupling theory for the Kardar-Parisi-Zhang equation
• Stretched exponential relaxation in the mode-coupling theory for the Kardar-Parisi-Zhang equation
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Cited by in corpus (10)

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• Nonperturbative renormalization group for the stationary Kardar-Parisi-Zhang equation: scaling functions and amplitude ratios in 1+1, 2+1 and 3+1 dimensions
• The Kardar-Parisi-Zhang equation in the weak noise limit: Pattern formation and upper critical dimension
• Anomalous scaling at non-thermal fixed points of Burgers' and Gross-Pitaevskii turbulence
• Power laws and stretched exponentials in a noisy finite-time-singularity model
• Roughening of the (1+1) interfaces in two-component surface growth with an admixture of random deposition
• Solitons in the noisy Burgers equation
• Correlations, soliton modes, and non-Hermitian linear mode transmutation in the 1D noisy Burgers equation
• Domain wall propagation and nucleation in a metastable two-level system
• Towards a strong coupling theory for the KPZ equation