| Abstract: |
| We investigate numerically the 1d focusing stochastic nonlinear Schrodinger (SNLS) equation with multiplicative or additive noise. We consider both the $L^2$ -critical and $L^2$-supercritical cases. We observe that for solutions that exist long time with positive probability, the energy grows linearly in time for both types of noise. We also study the time dependence of mass in the additive noise (while in the multiplicative noise it is conserved due to Stratonovich integral). For solutions which blow-up in finite time, we investigate the blow-up dynamics and find that once the process is driven into the blow-up regime, the blow-up dynamics (profile and rate) is similar to the deterministic case. We also compare solutions behavior for space time white noise versus space correlation. |
|