Stochastic Symplectic and Multi-Symplectic Methods for Nonlinear   Schr\"odinger Equation with White Noise Dispersion
  We indicate that the nonlinear Schr\"odinger equation with white noise dispersion possesses stochastic symplectic and multi-symplectic structures. Based on these structures, we propose the stochastic symplectic and multi-symplectic methods, which preserve the continuous and discrete charge conservation laws, respectively. Moreover, we show that the proposed methods are convergent with temporal order one in probability. Numerical experiments are presented to verify our theoretical results. 
Jianbo Cui, Jialin Hong, Zhihui Liu, Weien Zhou
math.NA