  In this paper, we discuss the different splitting approaches to solve the
Gross-Pitaevskii equation numerically. We consider conservative
finite-difference schemes and spectral methods for the spatial discretisation.
Further, we apply implicit or explicit time-integrators and combine such
schemes with different splitting approaches. The numerical solutions are
compared based on the conservation of the $L_2$-norm with the analytical
solutions. The advantages of the splitting methods for large time-domains are
presented in several numerical examples of different solitons applications.
