Conerservative and Nonconservative Schemes for the Solution of the Nonlinear Schrodinger Equation

Five methods for the integration in time of a semidiscretizationof the nonlinear Schrödinger equation are extensively tested.Three of them (a partly explicit scheme and two splitting procedures)are found to perform poorly. The reasons for their failure,including the so-called nonlinear blow-up, are analysed. Wedraw general conclusions on the advantages and drawbacks associatedwith the use of time-integrators which exactly conserve energy.