Optimal convergence and long-time conservation of exponential integration for Schrödinger equations in a normal or highly oscillatory regime.

摘要: In this paper, we formulate and analyse exponential integrations when applied to nonlinear Schrodinger equations in a normal or highly oscillatory regime. A kind of integrators with energy preservation, optimal convergence long time near conservations actions, momentum density will be formulated analysed. To end, derive continuous-stage show that the can exactly preserve Hamiltonian systems. Three practical energy-preserving are presented. It is shown these exhibit have over times. numerical experiment carried out support all theoretical results presented paper. Some applications other kinds ordinary/partial differential also