Modal and total power spectra of Nikolaevskii turbulence

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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 low-frequency 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.

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