Self-consistent approach to the Kardar-Parisi-Zhang equation

We propose a self-consistent treatment of the Kardar-Parisi-Zhang equation in d dimensions, in order to calculate the dynamical exponent z and the roughness exponent χ, and also amplitude ratios and subleading corrections. We assume that the dynamics of each mode is purely exponential, and find agreement with known results in d=1 and 2. For d>${\mathit{d}}^{\mathrm{*}}$≃2.85, however, none of our solutions is compatible with this assumption. Our method is distinct from, but akin to, the one recently proposed by M. Schwartz and S. F. Edwards [Europhys. Lett. 20, 301 (1992)].