This paper studies two examples of internal wave band temperature fluctuation spectra from moored instruments on the central Mexican Pacific Shelf and the western shelf of the Japan/East Sea. It is observed that for band f $ll$ ω $ll$ N, where N is the buoyancy frequency and f is the inertial frequency, the spectral falloff rate with frequency ω tends to ω-3. These features of spectra are simulated by the model spectrum of nonlinear internal waves in the shallow sea. It is shown that nonlinear internal waves with frequencies f $ll$ ω $ll$ N are governed by the modified simple wave equation. This equation underlie of the model spectrum of nonlinear internal waves on the shelf. The model spectrum shows ω-3 falloff rate with frequency in contrast with model spectrum proposed with Garrett and Munk, which shows ω-2 falloff rate.