COLLAPSE OF SOLITARY EXCITATIONS IN THE NONLINEAR SCHRODINGER-EQUATION WITH NONLINEAR DAMPING AND WHITE-NOISE

We study the effect of adding noise and nonlinear damping in the two-d imensional nonlinear Schrodinger equation (NLS). Using a collective ap proach, we find that for initial conditions where total collapse occur s in the unperturbed NLS, the presence of the damping term will instea d in an exponentially decreasing width of the solution in the long-tim e limit. We also find that a sufficiently large noise variance may cau se an initially localized distribution to spread instead of contractin g, and that the critical variance necessary to cause dispersion will f or small damping be the same as for the undamped system.