A numerical study of the perturbed semiclassical focusing nonlinear Schroedinger equation

In this Letter we undertake a numerical study of the problem of small perturbations of the so-called semiclassical limit of the focusing nonlinear Schroedinger (NLS) equation in 1+1 dimensions. These perturbations represent the effects of damping and forcing and render the NLS equation nonintegrable. Depending on the ratio of the two parameters associated with these effects a rich variety of phenomena are observed, ranging from stationary and traveling solitons to chaotic spatio-temporal oscillations