Effect of noise on extreme events probability in a one-dimensional nonlinear Schrödinger equation

• Multiplicative noise strongly increases probability of extreme events in 1D NLS.
• This is most pronounced for spatially correlated noise, even when nonlinearity is weak.
• Approximate Langevin equation for the L2L2-norm of the solution is derived.

We report a numerical observation that multiplicative random forcing (noise) significantly increases the probability of formation of extreme events in the one-dimensional, focusing nonlinear Schrödinger equation. Furthermore, this phenomenon is sensitive to the noise's spatial correlation length. Highly correlated multiplicative noise may increase the probability of extreme events even when the average nonlinearity of the system is weak. On the contrary, noise with short spatial correlations substantially increases the probability of extreme events only for sufficiently strong average nonlinearity.