Numerical Solution of the Mode-Coupling Equations for the Kardar-Parisi-Zhang Equation in One Dimension
Abstract
We have studied the Kardar-Parisi-Zhang equation in the strong coupling regime in the mode-coupling approximation. We solved numerically in dimension d=1 for the correlation function at wavevector k. At large times t we found the predicted stretched exponential decay consistent with our previous saddle point analysis in [Phys. Rev. E 63, 057103 (2001)], but we also observed that the decay to zero occurred in an unexpected oscillatory way. We have compared the results from mode-coupling for the scaling functions with the recent exact results from Praehofer and Spohn [cond-mat/0101200] for d=1 who also find an oscillatory decay to zero.
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