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Behaviour of solutions to the 1D focusing stochastic <i>L</i>2-critical and supercritical nonlinear Schrödinger equation with space-time white noise
We study the focusing stochastic nonlinear Schr\"odinger equation in 1D in the $L^2$-critical and supercritical cases with an additive or multiplicative perturbation driven by space-time white noise. Unlike the deterministic case, the Hamiltonian (or energy) is not conserved in the stochastic setting, nor is the mass (or the $L^2$-norm) conserved …