  We study null 1/4 BPS deformations of flat domain wall solutions (NDDW) in
N=2, d=5 gauged supergravity with hypermultiplets and vector multiplets
coupled. These are uncharged time-dependent configurations and contain as
special case, 1/2 supersymmetric flat domain walls (DW), as well as 1/2 BPS
null solutions of the ungauged supergravity. Combining our analysis with the
classification method initiated by Gauntlett et al., we prove that all the
possible deformations of the DW have origin in the hypermultiplet sector or/and
are null. Here, we classify all the null deformations: we show that they
naturally organize themselves into "gauging" (v-deformation) and "non gauging"
(u-deformation). They have different properties: only in presence of
v-deformation is the solution supported by a time-dependent scalar potential.
Furthermore we show that the number of possible deformations equals the number
of matter multiplets coupled. We discuss the general procedure for constructing
explicit solutions, stressing the crucial role taken by the integrability
conditions of the scalars as spacetime functions. Two analytical solutions are
presented. Finally, we comment on the holographic applications of the NDDW, in
relation to the recently proposed time-dependent AdS/CFT.
