Numerical solution of the mode-coupling equations for the Kardar-Parisi-Zhang equation in one dimension

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 wave vector 𝐤. At large times t we found the predicted stretched exponential decay consistent with our previous saddle point analysis [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 Prähofer and Spohn (e-print cond-mat/0101200) for 𝑑=1 who also find an oscillatory decay to zero.