Stochastic Symplectic and Multi-Symplectic Methods for Nonlinear Schrödinger Equation with White Noise Dispersion
This work provides structure-preserving numerical methods for stochastic partial differential equations, benefiting researchers in computational mathematics and physics.
The paper identifies stochastic symplectic and multi-symplectic structures in the nonlinear Schrödinger equation with white noise dispersion and proposes numerical methods that preserve charge conservation laws, achieving first-order temporal convergence in probability.
We indicate that the nonlinear Schrödinger 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.