Simulation of coherent structures in nonlinear Schrödinger-type equations

This paper presents some numerical methods to simulate the evolution of coherent structures with small fluctuations, that appear as typical solutions of a class of nonintegrable nonlinear Schrödinger equations. The construction of the methods is particularly focused on two points: on one hand, the generation of the ground state profiles, to be used in the initial data of the simulations, combines a suitable spatial discretization with the resolution of a discrete variational problem. On the other hand, the approximation to leading parameters of these structures is controlled by the time integration. We compare different methods when simulating the evolution of initial ground state profiles and some initial data perturbed from them.