标题： 一种新的半解析多不变量保持积分器用于守恒偏微分方程 显示英文标题

标题： A novel semi-analytical multiple invariants-preserving integrator for conservative PDEs

摘要： 许多守恒型偏微分方程，如 Korteweg-de Vries（KdV）方程、非线性 Schrödinger 方程和 Klein-Gordon 方程，都具有多个不变泛函。本文基于离散变分导数的定义，利用投影技术构造了一种新颖的半解析多不变量保持积分器，用于求解守恒型偏微分方程。所提出的积分器的精度与基础积分器相同。在应用方面，针对 KdV 方程推导出了一些具体的质量-动量-能量保持积分器。 显示英文摘要

摘要： Many conservative partial differential equations such as the Korteweg-de Vries (KdV) equation, and the nonlinear Schr\"{o}dinger equations, the Klein-Gordon equation have more than one invariant functionals. In this paper, we propose the definition of the discrete variational derivative, based on which, a novel semi-analytical multiple invariants-preserving integrator for the conservative partial differential equations is constructed by projection technique. The proposed integrators are shown to have the same order of accuracy as the underlying integrators. For applications, some concrete mass-momentum-energy-preserving integrators are derived for the KdV equation.