  The stability and dynamical properties of the so-called resonant nonlinear
Schr\"odinger (RNLS) equation, are considered. The RNLS is a variant of the
nonlinear Schr\"odinger (NLS) equation with the addition of a perturbation used
to describe wave propagation in cold collisionless plasmas. We first examine
the modulational stability of plane waves in the RNLS model, identifying the
modifications of the associated conditions from the NLS case. We then move to
the study of solitary waves with vanishing and nonzero boundary conditions.
Interestingly the RNLS, much like the usual NLS, exhibits both dark and bright
soliton solutions depending on the relative signs of dispersion and
nonlinearity. The corresponding existence, stability and dynamics of these
solutions are studied systematically in this work.
