Multi-symplectic methods for generalized Schroedinger equations

摘要

Recent results on spectral and finite difference multi-symplectic schemes for one- and two-dimensional PDEs are discussed. Multi-symplectic schemes for the one-dimensional nonlinear Schroedinger equation and the two-dimensional Gross-Pitaevskii equation are developed. The new schemes exactly preserve a discrete multi-symplectic conservation law. The conservation of local energy and momentum is examined as well as preservation of several global invariants.