We calculate the spectrum of linear perturbations of standing wave solutions
discussed in [Phys. Rev. D 87, 123006 (2013)], as the first step to investigate
the stability of globally regular, asymptotically AdS, time-periodic solutions
discovered in [Phys. Rev. Lett. 111 051102 (2013)]. We show that while this
spectrum is only asymptotically nondispersive (as contrasted with the pure AdS
case), putting a small standing wave solution on the top of AdS solution indeed
prevents the turbulent instability. Thus we support the idea advocated in
previous works that nondispersive character of the spectrum of linear
perturbations of AdS space is crucial for the conjectured turbulent
instability.Comment: 7 pages, 4 figures; v2: minor corrections in the tex
