  A classical scenario suggests that ULIRGs transform colliding spiral galaxies
into a spheroid dominated early-type galaxy. Recent high-resolution simulations
have instead shown that, under some circumstances, rotation disks can be
preserved during the merging process or rapidly regrown after coalescence. Our
goal is to analyze in detail the ionised gas kinematics in a sample of ULIRGs
to infer the incidence of gas rotational dynamics in late-stage interacting
galaxies and merger remnants. We analysed MUSE data of a sample of 20 nearby
(z<0.165) ULIRGs, as part of the "Physics of ULIRGs with MUSE and ALMA" (PUMA)
project. We found that 27% individual nuclei are associated with kpc-scale
disk-like gas motions. The rest of the sample displays a plethora of gas
kinematics, dominated by winds and merger-induced flows, which make the
detection of rotation signatures difficult. On the other hand, the incidence of
stellar disk-like motions is ~2 times larger than gaseous disks, as the former
are probably less affected by winds and streams. The eight galaxies with a
gaseous disk present relatively high intrinsic gas velocity dispersion (sigma =
30-85 km/s), rotationally-supported motions (with gas rotation velocity over
velocity dispersion vrot/sigma > 1-8), and dynamical masses in the range
(2-7)x1e10 Msun. By combining our results with those of local and high-z disk
galaxies from the literature, we found a significant correlation between sigma
and the offset from the main sequence (MS), after correcting for their
evolutionary trends. Our results confirm the presence of kpc-scale rotating
disks in interacting galaxies and merger remnants, with an incidence going from
27% (gas) to ~50% (stars). The ULIRGs gas velocity dispersion is up to a factor
of ~4 higher than in local normal MS galaxies, similar to high-z starbursts as
presented in the literature.
