Numerical study of the logarithmic Schrodinger equation with repulsive harmonic potential

More explanations. Final version.We consider the Schrodinger equation with alogarithmic nonlinearity and a repulsive harmonic potential. Dependingon the parameters of the equation, the solution may or may not bedispersive. When dispersion occurs, it does with an exponential ratein time. To control this, we change the unknown function through ageneralized lens transform. This approach neutralizes the possibleboundary effects, and could be used in the case of the Schrodingerequation without potential. We then employ standard splitting methods on the newequation via a nonuniform grid, after the logarithmic nonlinearity has been regularized. Wealso 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