Kardar-Parisi-Zhang equation with temporally correlated noise: A self-consistent approach

In this paper we discuss the well known Kardar-Parisi-Zhang (KPZ) equation driven by temporally correlated noise. We use a self-consistent approach to derive the scaling exponents of this system. We also draw general conclusions about the behavior of the dynamic structure factor Φq(t) as a function of time. The approach we use here generalizes the well known self-consistent expansion (SCE) that was used successfully in the case of the KPZ equation driven by white noise, but unlike SCE, it is not based on a Fokker-Planck form of the KPZ equation, but rather on its Langevin form. A comparison to two other analytical methods, as well as to the only numerical study of this problem is made, and a need for an updated extensive numerical study is identified. We also show that a generalization of this method to any spatiotemporal correlations in the noise is possible, and two examples of this kind are considered.