Long Time Numerical Approximation of Coherent-Structure Solutions of the Cubic Schrödinger Equation

The purpose of this work is to determine suitable numerical methods to simulate the evolution of coherent structures for the cubic nonlinear Schrodinger equation with Dirichlet boundary conditions on a finite one-dimensional interval. We consider different time integrators, some of them preserving one or two invariants of the problem. We show that the preservation of these invariants is essential for a good long time simulation.