  We examine conditions for finite-time collapse of the solutions of the
higher-order nonlinear Schr\"odinger (NLS) equation incorporating third-order
dispersion, self-steepening, linear and nonlinear gain and loss, and Raman
scattering; this is a system that appears in many physical contexts as a more
realistic generalization of the integrable NLS. By using energy arguments, it
is found that the collapse dynamics is chiefly controlled by the
linear/nonlinear gain/loss strengths. We identify a critical value of the
linear gain, separating the possible decay of solutions to the trivial
zero-state, from collapse. The numerical simulations, performed for a wide
class of initial data, are found to be in very good agreement with the
analytical results, and reveal long-time stability properties of localized
solutions. The role of the higher-order effects to the transient dynamics is
also revealed in these simulations.
