One-stage exponential integrators for nonlinear Schr\uf6dinger equations over long times

Near-conservation over long times of the actions, of the energy, of the mass and of the momentum along the numerical solution of the cubic Schr\uf6dinger equation with small initial data is shown. Spectral discretization in space and one-stage exponential integrators in time are used. The proofs use modulated Fourier expansions