By using ultrathin nonlinear media, the phase velocity of nonlinear polarization waves can be continuously adjusted. We realized nonlinear Cherenkov radiation (NCR) in an anomalous dispersion medium experimentally, which breaks the minimum speed limit of NCR. This modified nonlinear Cherenkov radiation has two new special states with respect to its prior, i.e., the degenerate state and extreme state. Also, periodically arranged ultrathin nonlinear media can enhance NCR and realize the nonlinear Smith-Purcell effect.