  We consider the Schrodinger equation with a logarithmic nonlinearity and a
repulsive harmonic potential. Depending on the parameters of the equation, the
solution may or may not be dispersive. When dispersion occurs, it does with an
exponential rate in time. To control this, we change the unknown function
through a generalized lens transform. This approach neutralizes the possible
boundary effects, and could be used in the case of the Schrodinger equation
without potential. We then employ standard splitting methods on the new
equation via a nonuniform grid, after the logarithmic nonlinearity has been
regularized. We also discuss the case of a power nonlinearity and give some
results concerning the error estimates of the first-order Lie-Trotter splitting
method for both cases of nonlinearities. Finally extensive numerical
experiments are reported to investigate the dynamics of the equations.
