Spectral splitting method for nonlinear Schrodinger equations with singular potential

We consider the time-dependent one-dimensional nonlinear Schro¨dinger equation with pointwise singular potential. Bymeans of spectral splitting methods we prove that the evolution operator is approximated by the Lie evolution operator,where the kernel of the Lie evolution operator is explicitly written. This result yields a numerical procedure which is muchless computationally expensive than multi-grid methods previously used. Furthermore, we apply the Lie approximation inorder to make some numerical experiments concerning the splitting of a soliton, interaction among solitons and blow-upphenomenon.