Long timenumerical approximation of coherent-structure solutions of the cubic schrödinger equation

Abstract

The purpose of this work is to determine suitable numerical methods to simulate the evolution of coherent structures for the cubic nonlinear Schrödinger equation with Dirichletboundary 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 ofthese invariants is essential for a good long time simulation.