  We theoretically and numerically study Bogoliubov-wave turbulence in
three-dimensional atomic Bose-Einstein condensates with the Gross-Pitaevskii
equation, investigating three spectra for the macroscopic wave function, the
density distribution, and the Bogoliubov-wave distribution. In this turbulence,
Bogoliubov waves play an important role in the behavior of these spectra, so
that we call it Bogoliubov-wave turbulence. In a previous study [D. Proment
\textit{et al.}, Phys. Rev. A \textbf{80}, 051603(R) (2009)], a $-3/2$ power
law in the spectrum for the macroscopic wave function was suggested by using
weak wave turbulence theory, but we find that another $-7/2$ power law appears
in both theoretical and numerical calculations. Furthermore, we focus on the
spectrum for the density distribution, which can be observed in experiments,
discussing the possibility of experimental observation. Through these
analytical and numerical calculations, we also demonstrate that the previously
neglected condensate dynamics induced by the Bogoliubov waves is remarkably
important.
