Modal and total power spectra of Nikolaevskii turbulence

We numerically investigate the modal and total time correlation functions and the corresponding power spectra for the Nikolaevskii equation. The modal power spectrum exhibits Lorentzian for lowfrequency ranges, while the total power spectrum diverges in the low-frequency limit. The dynamic exponent is equal to 2 and 3/2 for smaller and larger system sizes, respectively. The relationship between the Nikolaevskii turbulence and the soft-mode turbulence is also discussed.