标题： 时间高阶统一的弱非线性薛定谔方程和波湍流格式 显示英文标题

标题： High order uniform in time schemes for weakly nonlinear Schrödinger equation and wave turbulence

摘要： 我们引入了两种多尺度数值方案，用于弱非线性薛定谔方程的时间积分，这些方案基于解的皮卡迭代的离散化。 这些高阶方案设计用于在特定的CFL条件下，相对于小非线性参数实现高精度。 通过利用这些方案的散射特性，借助低频投影线性流，我们还建立了其在长时间范围内的统一精度。 提供了数值模拟来说明理论结果，并且这些方案进一步被应用于波湍流框架下的动力学研究。 显示英文摘要

摘要： We introduce two multiscale numerical schemes for the time integration of weakly nonlinear Schr\"odinger equations, built upon the discretization of Picard iterates of the solution. These high-order schemes are designed to achieve high precision with respect to the small nonlinearity parameter under particular CFL condition. By exploiting the scattering properties of these schemes thanks to a low-frequency projected linear flow, we also establish its uniform accuracy over long time horizons. Numerical simulations are provided to illustrate the theoretical results, and these schemes are further applied to investigate dynamics in the framework of wave turbulence.