  The defocusing nonlinear Schr\"odinger (NLS) equation has no the modulational
instability, and was not found to possess the rogue wave (RW) phenomenon up to
now. In this paper, we firstly investigate some novel nonlinear wave structures
in the defocusing NLS equation with real-valued time-dependent and
time-independent potentials such that the stable new RWs and W-shaped solitons
are found, respectively. Moreover, the interactions of two or three RWs are
explored such that the RWs with higher amplitudes are generated in the
defocusing NLS equation with real-valued time-dependent potentials. Finally, we
study the defocusing NLS equation with complex PT -symmetric potentials such
that some RWs and W-shaped solitons are also found. These novel results will be
useful to design the related physical experiments to generate the RW phenomena
and W-shaped solitons in the case of defocusing nonlinear interactions, and to
apply them in the related fields of nonlinear or even linear sciences.
