  The generation of rogue waves is investigated via a nonlocal nonlinear
Schrodinger (NLS) equation. In this system, modulation instability is
suppressed and is usually expected that rogue wave formation would also be
limited. On the contrary, a parameter regime is identified where the
instability is suppressed but nevertheless the number and amplitude of the
rogue events increase, as compared to the standard NLS (which is a limit of the
nonlocal system). Furthermore, the nature of these waves is investigated; while
no analytical solutions are known to model these events, numerically it is
shown that they differ significantly from either the rational (Peregrine) or
soliton solution of the limiting NLS equation. As such, these findings may also
help in rogue wave realization experimentally in these media.
