  We consider the nonlinear Schr{\"o}dinger-Langevin equation for both signs of
the logarithmic nonlinearity. We explicitly compute the dynamics of Gaussian
solutions for large times, which is obtained through the study of a particular
nonlinear differential equation of order 2. We then give the asymptotic
behavior of general energy weak solutions under some regularity assumptions.
Some numerical simulations are performed in order to corroborate the
theoretical results.
